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Mixed integer linear problem - Revision history
2026-05-26T09:09:10Z
Revision history for this page on the wiki
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https://wiki.openmod-initiative.org/index.php?title=Mixed_integer_linear_problem&diff=11201&oldid=prev
Lilly Schoen at 08:54, 10 November 2017
2017-11-10T08:54:42Z
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>|Definition=A mixed-integer linear program is a problem with</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>|Definition=A mixed-integer linear program is a problem with</div></td></tr>
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<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div>- <del class="diffchange diffchange-inline">Linear </del>objective function, fTx, where f is a column vector of constants, and x is the column vector of unknowns</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>- <ins class="diffchange diffchange-inline">linear </ins>objective function, fTx, where f is a column vector of constants, and x is the column vector of unknowns</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div>- <del class="diffchange diffchange-inline">Bounds </del>and linear constraints, but no nonlinear constraints (for definitions, see Write Constraints)</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>- <ins class="diffchange diffchange-inline">bounds </ins>and linear constraints, but no nonlinear constraints (for definitions, see Write Constraints)</div></td></tr>
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<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div>- <del class="diffchange diffchange-inline">Restrictions </del>on some components of x to have integer values</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>- <ins class="diffchange diffchange-inline">restrictions </ins>on some components of x to have integer values</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>In mathematical terms, given vectors f, lb, and ub, matrices A and Aeq, corresponding vectors b and beq, and a set of indices intcon, find a vector x to solve.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>In mathematical terms, given vectors f, lb, and ub, matrices A and Aeq, corresponding vectors b and beq, and a set of indices intcon, find a vector x to solve.</div></td></tr>
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Lilly Schoen
https://wiki.openmod-initiative.org/index.php?title=Mixed_integer_linear_problem&diff=11198&oldid=prev
Lilly Schoen at 08:54, 10 November 2017
2017-11-10T08:54:08Z
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>|Sources=https://de.mathworks.com/help/optim/ug/mixed-integer-linear-programming-algorithms.html?requestedDomain=www.mathworks.com#btv2z9c</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>|Sources=https://de.mathworks.com/help/optim/ug/mixed-integer-linear-programming-algorithms.html?requestedDomain=www.mathworks.com#btv2z9c</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>}}</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>}}</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div><span><span class="MathEquation" style="font-size: 15px"><span class="MathRoot HBox" style="display: inline-block;  position: relative"><span class="MathRow HBox" style="display: inline-block;  position: relative;  font-size: 15px"><span class="MathScript VBox" style="display: inline-block;  position: relative;  text-align: center;  vertical-align: -12px"><span class="MathRow HBox" style="display: block;  position: relative;  font-size: 15px;  margin-top: 0px"><span class="MathText MathTextBox code" style="position: relative;  font-style: normal">min</span></span><span class="MathRow HBox" style="display: block;  position: relative;  font-size: 10px;  margin-top: 0px"><span class="MathText MathTextBox text" style="position: relative">x</span></span></span><span class="MathScript HBox" style="display: inline-block;  position: relative;  font-size: 15px;  margin-left: 0.222222em"><span class="MathRow HBox" style="display: inline-block;  position: relative;  font-size: 15px"><span class="MathText MathTextBox text" style="position: relative;  margin-left: 0.2em;  margin-right: 0.2em">f</span></span><span class="VBox" style="display: inline-block;  position: relative;  text-align: left;  vertical-align: 5px"><span class="MathRow HBox" style="display: block;  position: relative;  font-size: 10px;  margin-top: 0px"><span class="MathText MathTextBox text" style="position: relative;  margin-right: 0.1em">T</span></span></span></span><span class="MathText MathTextBox text" style="position: relative;  margin-left: 0.05em">x</span><span class="MathText MathTextBox mtext" style="position: relative;  font-style: normal">&nbsp;subject&nbsp;to {</span><span class="MathRow HBox" style="display: inline-block;  position: relative;  font-size: 15px"><span class="MathDelimiter StretchyBox" style="display: inline-block;  position: relative;  text-align: center;  height: 78px;  width: 13px;  vertical-align: -34px"></span><span class="MathRow HBox" style="display: inline-block;  position: relative;  font-size: 15px"><span class="MathMatrix VBox" style="display: inline-block;  position: relative;  text-align: center;  vertical-align: -31px"><span class="HBox" style="display: block;  position: relative;  margin-top: 0px"><span class="VBox" style="display: inline-block;  position: relative;  text-align: left;  vertical-align: 0px"><span class="HBox" style="display: block;  position: relative;  margin-top: 0px"><span class="MathRow HBox" style="display: inline-block;  position: relative;  font-size: 15px"><span class="MathText MathTextBox text" style="position: relative;  margin-left: 0.05em">x</span><span class="MathRow HBox" style="display: inline-block;  position: relative;  font-size: 15px"><span class="MathText MathTextBox extra1" style="position: relative">(</span><span class="MathText MathTextBox mtext" style="position: relative;  font-style: normal">intcon</span><span class="MathText MathTextBox extra1" style="position: relative">)</span></span><span class="MathText MathTextBox mtext" style="position: relative;  font-style: normal">&nbsp;are&nbsp;integers</span></span><span class="WhiteSpaceBox" style="display: inline-block;  position: relative;  margin-left: 0px"></span></span><span class="HBox" style="display: block;  position: relative;  margin-top: 0px"><span class="VBox" style="display: inline-block;  position: relative;  height: 21px;  vertical-align: -6px"></span><span class="MathRow HBox" style="display: inline-block;  position: relative;  font-size: 15px"><span class="MathText MathTextBox text" style="position: relative;  margin-left: 0.1em">A</span><span class="MathText MathTextBox symbol" style="position: relative;  margin-left: 0.222222em">⋅</span><span class="MathText MathTextBox text" style="position: relative;  margin-left: 0.272222em">x</span><span class="MathText MathTextBox symbol" style="position: relative;  margin-left: 0.277778em">≤</span><span class="MathText MathTextBox text" style="position: relative;  margin-left: 0.277778em">b</span></span><span class="WhiteSpaceBox" style="display: inline-block;  position: relative;  margin-left: 0px"></span></span><span class="HBox" style="display: block;  position: relative;  margin-top: 0px"><span class="VBox" style="display: inline-block;  position: relative;  height: 21px;  vertical-align: -6px"></span><span class="MathRow HBox" style="display: inline-block;  position: relative;  font-size: 15px"><span class="MathText MathTextBox text" style="position: relative;  margin-left: 0.1em">A</span><span class="MathText MathTextBox text" style="position: relative">e</span><span class="MathText MathTextBox text" style="position: relative">q</span><span class="MathText MathTextBox symbol" style="position: relative;  margin-left: 0.222222em">⋅</span><span class="MathText MathTextBox text" style="position: relative;  margin-left: 0.272222em">x</span><span class="MathText MathTextBox symbol" style="position: relative;  margin-left: 0.277778em">=</span><span class="MathText MathTextBox text" style="position: relative;  margin-left: 0.277778em">b</span><span class="MathText MathTextBox text" style="position: relative">e</span><span class="MathText MathTextBox text" style="position: relative">q</span></span></span><span class="HBox" style="display: block;  position: relative;  margin-top: 0px"><span class="MathRow HBox" style="display: inline-block;  position: relative;  font-size: 15px"><span class="MathText MathTextBox text" style="position: relative">l</span><span class="MathText MathTextBox text" style="position: relative">b</span><span class="MathText MathTextBox symbol" style="position: relative;  margin-left: 0.277778em">≤</span><span class="MathText MathTextBox text" style="position: relative;  margin-left: 0.327778em">x</span><span class="MathText MathTextBox symbol" style="position: relative;  margin-left: 0.277778em">≤</span><span class="MathText MathTextBox text" style="position: relative;  margin-left: 0.277778em">u</span><span class="MathText MathTextBox text" style="position: relative">b</span><span class="MathText MathTextBox symbol" style="position: relative">.</span></span></span></span></span></span></span></span></span></span></span></span></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><span><span class="MathEquation" style="font-size: 15px"><span class="MathRoot HBox" style="display: inline-block;  position: relative"><span class="MathRow HBox" style="display: inline-block;  position: relative;  font-size: 15px"><span class="MathScript VBox" style="display: inline-block;  position: relative;  text-align: center;  vertical-align: -12px"><span class="MathRow HBox" style="display: block;  position: relative;  font-size: 15px;  margin-top: 0px"><span class="MathText MathTextBox code" style="position: relative;  font-style: normal">min</span></span><span class="MathRow HBox" style="display: block;  position: relative;  font-size: 10px;  margin-top: 0px"><span class="MathText MathTextBox text" style="position: relative">x</span></span></span><span class="MathScript HBox" style="display: inline-block;  position: relative;  font-size: 15px;  margin-left: 0.222222em"><span class="MathRow HBox" style="display: inline-block;  position: relative;  font-size: 15px"><span class="MathText MathTextBox text" style="position: relative;  margin-left: 0.2em;  margin-right: 0.2em">f</span></span><span class="VBox" style="display: inline-block;  position: relative;  text-align: left;  vertical-align: 5px"><span class="MathRow HBox" style="display: block;  position: relative;  font-size: 10px;  margin-top: 0px"><span class="MathText MathTextBox text" style="position: relative;  margin-right: 0.1em">T</span></span></span></span><span class="MathText MathTextBox text" style="position: relative;  margin-left: 0.05em">x</span><span class="MathText MathTextBox mtext" style="position: relative;  font-style: normal">&nbsp;subject&nbsp;to {</span><span class="MathRow HBox" style="display: inline-block;  position: relative;  font-size: 15px"><span class="MathDelimiter StretchyBox" style="display: inline-block;  position: relative;  text-align: center;  height: 78px;  width: 13px;  vertical-align: -34px"></span><span class="MathRow HBox" style="display: inline-block;  position: relative;  font-size: 15px"><span class="MathMatrix VBox" style="display: inline-block;  position: relative;  text-align: center;  vertical-align: -31px"><span class="HBox" style="display: block;  position: relative;  margin-top: 0px"><span class="VBox" style="display: inline-block;  position: relative;  text-align: left;  vertical-align: 0px"><span class="HBox" style="display: block;  position: relative;  margin-top: 0px"><span class="MathRow HBox" style="display: inline-block;  position: relative;  font-size: 15px"><span class="MathText MathTextBox text" style="position: relative;  margin-left: 0.05em">x</span><span class="MathRow HBox" style="display: inline-block;  position: relative;  font-size: 15px"><span class="MathText MathTextBox extra1" style="position: relative">(</span><span class="MathText MathTextBox mtext" style="position: relative;  font-style: normal">intcon</span><span class="MathText MathTextBox extra1" style="position: relative">)</span></span><span class="MathText MathTextBox mtext" style="position: relative;  font-style: normal">&nbsp;are&nbsp;integers</span></span><span class="WhiteSpaceBox" style="display: inline-block;  position: relative;  margin-left: 0px"></span></span><span class="HBox" style="display: block;  position: relative;  margin-top: 0px"><span class="VBox" style="display: inline-block;  position: relative;  height: 21px;  vertical-align: -6px"></span><span class="MathRow HBox" style="display: inline-block;  position: relative;  font-size: 15px"><span class="MathText MathTextBox text" style="position: relative;  margin-left: 0.1em">A</span><span class="MathText MathTextBox symbol" style="position: relative;  margin-left: 0.222222em">⋅</span><span class="MathText MathTextBox text" style="position: relative;  margin-left: 0.272222em">x</span><span class="MathText MathTextBox symbol" style="position: relative;  margin-left: 0.277778em">≤</span><span class="MathText MathTextBox text" style="position: relative;  margin-left: 0.277778em">b</span></span><span class="WhiteSpaceBox" style="display: inline-block;  position: relative;  margin-left: 0px"></span></span><span class="HBox" style="display: block;  position: relative;  margin-top: 0px"><span class="VBox" style="display: inline-block;  position: relative;  height: 21px;  vertical-align: -6px"></span><span class="MathRow HBox" style="display: inline-block;  position: relative;  font-size: 15px"><span class="MathText MathTextBox text" style="position: relative;  margin-left: 0.1em">A</span><span class="MathText MathTextBox text" style="position: relative">e</span><span class="MathText MathTextBox text" style="position: relative">q</span><span class="MathText MathTextBox symbol" style="position: relative;  margin-left: 0.222222em">⋅</span><span class="MathText MathTextBox text" style="position: relative;  margin-left: 0.272222em">x</span><span class="MathText MathTextBox symbol" style="position: relative;  margin-left: 0.277778em">=</span><span class="MathText MathTextBox text" style="position: relative;  margin-left: 0.277778em">b</span><span class="MathText MathTextBox text" style="position: relative">e</span><span class="MathText MathTextBox text" style="position: relative">q</span></span></span><span class="HBox" style="display: block;  position: relative;  margin-top: 0px"><span class="MathRow HBox" style="display: inline-block;  position: relative;  font-size: 15px"><span class="MathText MathTextBox text" style="position: relative">l</span><span class="MathText MathTextBox text" style="position: relative">b</span><span class="MathText MathTextBox symbol" style="position: relative;  margin-left: 0.277778em">≤</span><span class="MathText MathTextBox text" style="position: relative;  margin-left: 0.327778em">x</span><span class="MathText MathTextBox symbol" style="position: relative;  margin-left: 0.277778em">≤</span><span class="MathText MathTextBox text" style="position: relative;  margin-left: 0.277778em">u</span><span class="MathText MathTextBox text" style="position: relative">b</span><span class="MathText MathTextBox symbol" style="position: relative">.</span></span></span></span></span></span></span></span></span></span></span></span<ins class="diffchange diffchange-inline">><br/</ins>></div></td></tr>
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Lilly Schoen
https://wiki.openmod-initiative.org/index.php?title=Mixed_integer_linear_problem&diff=11195&oldid=prev
Lilly Schoen at 08:52, 10 November 2017
2017-11-10T08:52:53Z
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<td colspan='2' style="background-color: white; color:black;">← Older revision</td>
<td colspan='2' style="background-color: white; color:black;">Revision as of 08:52, 10 November 2017</td>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>|Sources=https://de.mathworks.com/help/optim/ug/mixed-integer-linear-programming-algorithms.html?requestedDomain=www.mathworks.com#btv2z9c</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>|Sources=https://de.mathworks.com/help/optim/ug/mixed-integer-linear-programming-algorithms.html?requestedDomain=www.mathworks.com#btv2z9c</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>}}</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>}}</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div><span><span class="MathEquation" style="font-size: 15px"><span class="MathRoot HBox" style="display: inline-block;  position: relative"><span class="MathRow HBox" style="display: inline-block;  position: relative;  font-size: 15px"><span class="MathScript VBox" style="display: inline-block;  position: relative;  text-align: center;  vertical-align: -12px"><span class="MathRow HBox" style="display: block;  position: relative;  font-size: 15px;  margin-top: 0px"><span class="MathText MathTextBox code" style="position: relative;  font-style: normal">min</span></span><span class="MathRow HBox" style="display: block;  position: relative;  font-size: 10px;  margin-top: 0px"><span class="MathText MathTextBox text" style="position: relative">x</span></span></span><span class="MathScript HBox" style="display: inline-block;  position: relative;  font-size: 15px;  margin-left: 0.222222em"><span class="MathRow HBox" style="display: inline-block;  position: relative;  font-size: 15px"><span class="MathText MathTextBox text" style="position: relative;  margin-left: 0.2em;  margin-right: 0.2em">f</span></span><span class="VBox" style="display: inline-block;  position: relative;  text-align: left;  vertical-align: 5px"><span class="MathRow HBox" style="display: block;  position: relative;  font-size: 10px;  margin-top: 0px"><span class="MathText MathTextBox text" style="position: relative;  margin-right: 0.1em">T</span></span></span></span><span class="MathText MathTextBox text" style="position: relative;  margin-left: 0.05em">x</span><span class="MathText MathTextBox mtext" style="position: relative;  font-style: normal">&nbsp;subject&nbsp;to<del class="diffchange diffchange-inline">&nbsp;</del></span><span class="MathRow HBox" style="display: inline-block;  position: relative;  font-size: 15px"><span class="MathDelimiter StretchyBox" style="display: inline-block;  position: relative;  text-align: center;  height: 78px;  width: 13px;  vertical-align: -34px"<del class="diffchange diffchange-inline">><span class="MathTextBox extra" style="position: absolute;  margin-left: 0.2775em;  display: block;  top: -1px"></span><span class="MathTextBox extra" style="position: absolute;  margin-left: 0.2775em;  display: block;  top: 12px"></span><span class="MathTextBox extra" style="position: absolute;  margin-left: 0.2775em;  display: block;  top: 16px"></span><span class="MathTextBox extra" style="position: absolute;  margin-left: 0.2775em;  display: block;  top: 21px"></span><span class="MathTextBox extra" style="position: absolute;  margin-left: 0.2775em;  display: block;  top: 25px"></span><span class="MathTextBox extra" style="position: absolute;  margin-left: 0.2775em;  display: block;  top: 51px"></span><span class="MathTextBox extra" style="position: absolute;  margin-left: 0.2775em;  display: block;  top: 56px"></span><span class="MathTextBox extra" style="position: absolute;  margin-left: 0.2775em;  display: block;  top: 60px"></span><span class="MathTextBox extra" style="position: absolute;  margin-left: 0.2775em;  display: block;  top: 64px"></span</del>></span><span class="MathRow HBox" style="display: inline-block;  position: relative;  font-size: 15px"><span class="MathMatrix VBox" style="display: inline-block;  position: relative;  text-align: center;  vertical-align: -31px"><span class="HBox" style="display: block;  position: relative;  margin-top: 0px"><span class="VBox" style="display: inline-block;  position: relative;  text-align: left;  vertical-align: 0px"><span class="HBox" style="display: block;  position: relative;  margin-top: 0px"<del class="diffchange diffchange-inline">><span class="VBox" style="display: inline-block;  position: relative;  height: 18px;  vertical-align: -6px"></span</del>><span class="MathRow HBox" style="display: inline-block;  position: relative;  font-size: 15px"><span class="MathText MathTextBox text" style="position: relative;  margin-left: 0.05em">x</span><span class="MathRow HBox" style="display: inline-block;  position: relative;  font-size: 15px"><span class="MathText MathTextBox extra1" style="position: relative">(</span><span class="MathText MathTextBox mtext" style="position: relative;  font-style: normal">intcon</span><span class="MathText MathTextBox extra1" style="position: relative">)</span></span><span class="MathText MathTextBox mtext" style="position: relative;  font-style: normal">&nbsp;are&nbsp;integers</span></span><span class="WhiteSpaceBox" style="display: inline-block;  position: relative;  margin-left: 0px"></span></span><span class="HBox" style="display: block;  position: relative;  margin-top: 0px"><span class="VBox" style="display: inline-block;  position: relative;  height: 21px;  vertical-align: -6px"></span><span class="MathRow HBox" style="display: inline-block;  position: relative;  font-size: 15px"><span class="MathText MathTextBox text" style="position: relative;  margin-left: 0.1em">A</span><span class="MathText MathTextBox symbol" style="position: relative;  margin-left: 0.222222em">⋅</span><span class="MathText MathTextBox text" style="position: relative;  margin-left: 0.272222em">x</span><span class="MathText MathTextBox symbol" style="position: relative;  margin-left: 0.277778em">≤</span><span class="MathText MathTextBox text" style="position: relative;  margin-left: 0.277778em">b</span></span><span class="WhiteSpaceBox" style="display: inline-block;  position: relative;  margin-left: 0px"></span></span><span class="HBox" style="display: block;  position: relative;  margin-top: 0px"><span class="VBox" style="display: inline-block;  position: relative;  height: 21px;  vertical-align: -6px"></span><span class="MathRow HBox" style="display: inline-block;  position: relative;  font-size: 15px"><span class="MathText MathTextBox text" style="position: relative;  margin-left: 0.1em">A</span><span class="MathText MathTextBox text" style="position: relative">e</span><span class="MathText MathTextBox text" style="position: relative">q</span><span class="MathText MathTextBox symbol" style="position: relative;  margin-left: 0.222222em">⋅</span><span class="MathText MathTextBox text" style="position: relative;  margin-left: 0.272222em">x</span><span class="MathText MathTextBox symbol" style="position: relative;  margin-left: 0.277778em">=</span><span class="MathText MathTextBox text" style="position: relative;  margin-left: 0.277778em">b</span><span class="MathText MathTextBox text" style="position: relative">e</span><span class="MathText MathTextBox text" style="position: relative">q</span<del class="diffchange diffchange-inline">></span><span class="WhiteSpaceBox" style="display: inline-block;  position: relative;  margin-left: 0px"</del>></span></span><span class="HBox" style="display: block;  position: relative;  margin-top: 0px"<del class="diffchange diffchange-inline">><span class="VBox" style="display: inline-block;  position: relative;  height: 18px;  vertical-align: -3px"></span</del>><span class="MathRow HBox" style="display: inline-block;  position: relative;  font-size: 15px"><span class="MathText MathTextBox text" style="position: relative">l</span><span class="MathText MathTextBox text" style="position: relative">b</span><span class="MathText MathTextBox symbol" style="position: relative;  margin-left: 0.277778em">≤</span><span class="MathText MathTextBox text" style="position: relative;  margin-left: 0.327778em">x</span><span class="MathText MathTextBox symbol" style="position: relative;  margin-left: 0.277778em">≤</span><span class="MathText MathTextBox text" style="position: relative;  margin-left: 0.277778em">u</span><span class="MathText MathTextBox text" style="position: relative">b</span><span class="MathText MathTextBox symbol" style="position: relative">.</span></span></span></span></span></span></span></span></span></span></span></span></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><span><span class="MathEquation" style="font-size: 15px"><span class="MathRoot HBox" style="display: inline-block;  position: relative"><span class="MathRow HBox" style="display: inline-block;  position: relative;  font-size: 15px"><span class="MathScript VBox" style="display: inline-block;  position: relative;  text-align: center;  vertical-align: -12px"><span class="MathRow HBox" style="display: block;  position: relative;  font-size: 15px;  margin-top: 0px"><span class="MathText MathTextBox code" style="position: relative;  font-style: normal">min</span></span><span class="MathRow HBox" style="display: block;  position: relative;  font-size: 10px;  margin-top: 0px"><span class="MathText MathTextBox text" style="position: relative">x</span></span></span><span class="MathScript HBox" style="display: inline-block;  position: relative;  font-size: 15px;  margin-left: 0.222222em"><span class="MathRow HBox" style="display: inline-block;  position: relative;  font-size: 15px"><span class="MathText MathTextBox text" style="position: relative;  margin-left: 0.2em;  margin-right: 0.2em">f</span></span><span class="VBox" style="display: inline-block;  position: relative;  text-align: left;  vertical-align: 5px"><span class="MathRow HBox" style="display: block;  position: relative;  font-size: 10px;  margin-top: 0px"><span class="MathText MathTextBox text" style="position: relative;  margin-right: 0.1em">T</span></span></span></span><span class="MathText MathTextBox text" style="position: relative;  margin-left: 0.05em">x</span><span class="MathText MathTextBox mtext" style="position: relative;  font-style: normal">&nbsp;subject&nbsp;to <ins class="diffchange diffchange-inline">{</ins></span><span class="MathRow HBox" style="display: inline-block;  position: relative;  font-size: 15px"><span class="MathDelimiter StretchyBox" style="display: inline-block;  position: relative;  text-align: center;  height: 78px;  width: 13px;  vertical-align: -34px"></span><span class="MathRow HBox" style="display: inline-block;  position: relative;  font-size: 15px"><span class="MathMatrix VBox" style="display: inline-block;  position: relative;  text-align: center;  vertical-align: -31px"><span class="HBox" style="display: block;  position: relative;  margin-top: 0px"><span class="VBox" style="display: inline-block;  position: relative;  text-align: left;  vertical-align: 0px"><span class="HBox" style="display: block;  position: relative;  margin-top: 0px"><span class="MathRow HBox" style="display: inline-block;  position: relative;  font-size: 15px"><span class="MathText MathTextBox text" style="position: relative;  margin-left: 0.05em">x</span><span class="MathRow HBox" style="display: inline-block;  position: relative;  font-size: 15px"><span class="MathText MathTextBox extra1" style="position: relative">(</span><span class="MathText MathTextBox mtext" style="position: relative;  font-style: normal">intcon</span><span class="MathText MathTextBox extra1" style="position: relative">)</span></span><span class="MathText MathTextBox mtext" style="position: relative;  font-style: normal">&nbsp;are&nbsp;integers</span></span><span class="WhiteSpaceBox" style="display: inline-block;  position: relative;  margin-left: 0px"></span></span><span class="HBox" style="display: block;  position: relative;  margin-top: 0px"><span class="VBox" style="display: inline-block;  position: relative;  height: 21px;  vertical-align: -6px"></span><span class="MathRow HBox" style="display: inline-block;  position: relative;  font-size: 15px"><span class="MathText MathTextBox text" style="position: relative;  margin-left: 0.1em">A</span><span class="MathText MathTextBox symbol" style="position: relative;  margin-left: 0.222222em">⋅</span><span class="MathText MathTextBox text" style="position: relative;  margin-left: 0.272222em">x</span><span class="MathText MathTextBox symbol" style="position: relative;  margin-left: 0.277778em">≤</span><span class="MathText MathTextBox text" style="position: relative;  margin-left: 0.277778em">b</span></span><span class="WhiteSpaceBox" style="display: inline-block;  position: relative;  margin-left: 0px"></span></span><span class="HBox" style="display: block;  position: relative;  margin-top: 0px"><span class="VBox" style="display: inline-block;  position: relative;  height: 21px;  vertical-align: -6px"></span><span class="MathRow HBox" style="display: inline-block;  position: relative;  font-size: 15px"><span class="MathText MathTextBox text" style="position: relative;  margin-left: 0.1em">A</span><span class="MathText MathTextBox text" style="position: relative">e</span><span class="MathText MathTextBox text" style="position: relative">q</span><span class="MathText MathTextBox symbol" style="position: relative;  margin-left: 0.222222em">⋅</span><span class="MathText MathTextBox text" style="position: relative;  margin-left: 0.272222em">x</span><span class="MathText MathTextBox symbol" style="position: relative;  margin-left: 0.277778em">=</span><span class="MathText MathTextBox text" style="position: relative;  margin-left: 0.277778em">b</span><span class="MathText MathTextBox text" style="position: relative">e</span><span class="MathText MathTextBox text" style="position: relative">q</span></span></span><span class="HBox" style="display: block;  position: relative;  margin-top: 0px"><span class="MathRow HBox" style="display: inline-block;  position: relative;  font-size: 15px"><span class="MathText MathTextBox text" style="position: relative">l</span><span class="MathText MathTextBox text" style="position: relative">b</span><span class="MathText MathTextBox symbol" style="position: relative;  margin-left: 0.277778em">≤</span><span class="MathText MathTextBox text" style="position: relative;  margin-left: 0.327778em">x</span><span class="MathText MathTextBox symbol" style="position: relative;  margin-left: 0.277778em">≤</span><span class="MathText MathTextBox text" style="position: relative;  margin-left: 0.277778em">u</span><span class="MathText MathTextBox text" style="position: relative">b</span><span class="MathText MathTextBox symbol" style="position: relative">.</span></span></span></span></span></span></span></span></span></span></span></span></div></td></tr>
</table>
Lilly Schoen
https://wiki.openmod-initiative.org/index.php?title=Mixed_integer_linear_problem&diff=11193&oldid=prev
Lilly Schoen at 08:51, 10 November 2017
2017-11-10T08:51:23Z
<p></p>
<table class='diff diff-contentalign-left'>
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<td colspan='2' style="background-color: white; color:black;">← Older revision</td>
<td colspan='2' style="background-color: white; color:black;">Revision as of 08:51, 10 November 2017</td>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>- Restrictions on some components of x to have integer values</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>- Restrictions on some components of x to have integer values</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div>In mathematical terms, given vectors f, lb, and ub, matrices A and Aeq, corresponding vectors b and beq, and a set of indices intcon, find a vector x to solve</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>In mathematical terms, given vectors f, lb, and ub, matrices A and Aeq, corresponding vectors b and beq, and a set of indices intcon, find a vector x to solve<ins class="diffchange diffchange-inline">.</ins></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div> </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del class="diffchange diffchange-inline">minxfTx subject to x(intcon) are integersA⋅x≤bAeq⋅x=beqlb≤x≤ub</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>|Sources=https://de.mathworks.com/help/optim/ug/mixed-integer-linear-programming-algorithms.html?requestedDomain=www.mathworks.com#btv2z9c</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>|Sources=https://de.mathworks.com/help/optim/ug/mixed-integer-linear-programming-algorithms.html?requestedDomain=www.mathworks.com#btv2z9c</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>}}</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>}}</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"><span><span class="MathEquation" style="font-size: 15px"><span class="MathRoot HBox" style="display: inline-block;  position: relative"><span class="MathRow HBox" style="display: inline-block;  position: relative;  font-size: 15px"><span class="MathScript VBox" style="display: inline-block;  position: relative;  text-align: center;  vertical-align: -12px"><span class="MathRow HBox" style="display: block;  position: relative;  font-size: 15px;  margin-top: 0px"><span class="MathText MathTextBox code" style="position: relative;  font-style: normal">min</span></span><span class="MathRow HBox" style="display: block;  position: relative;  font-size: 10px;  margin-top: 0px"><span class="MathText MathTextBox text" style="position: relative">x</span></span></span><span class="MathScript HBox" style="display: inline-block;  position: relative;  font-size: 15px;  margin-left: 0.222222em"><span class="MathRow HBox" style="display: inline-block;  position: relative;  font-size: 15px"><span class="MathText MathTextBox text" style="position: relative;  margin-left: 0.2em;  margin-right: 0.2em">f</span></span><span class="VBox" style="display: inline-block;  position: relative;  text-align: left;  vertical-align: 5px"><span class="MathRow HBox" style="display: block;  position: relative;  font-size: 10px;  margin-top: 0px"><span class="MathText MathTextBox text" style="position: relative;  margin-right: 0.1em">T</span></span></span></span><span class="MathText MathTextBox text" style="position: relative;  margin-left: 0.05em">x</span><span class="MathText MathTextBox mtext" style="position: relative;  font-style: normal">&nbsp;subject&nbsp;to&nbsp;</span><span class="MathRow HBox" style="display: inline-block;  position: relative;  font-size: 15px"><span class="MathDelimiter StretchyBox" style="display: inline-block;  position: relative;  text-align: center;  height: 78px;  width: 13px;  vertical-align: -34px"><span class="MathTextBox extra" style="position: absolute;  margin-left: 0.2775em;  display: block;  top: -1px"></span><span class="MathTextBox extra" style="position: absolute;  margin-left: 0.2775em;  display: block;  top: 12px"></span><span class="MathTextBox extra" style="position: absolute;  margin-left: 0.2775em;  display: block;  top: 16px"></span><span class="MathTextBox extra" style="position: absolute;  margin-left: 0.2775em;  display: block;  top: 21px"></span><span class="MathTextBox extra" style="position: absolute;  margin-left: 0.2775em;  display: block;  top: 25px"></span><span class="MathTextBox extra" style="position: absolute;  margin-left: 0.2775em;  display: block;  top: 51px"></span><span class="MathTextBox extra" style="position: absolute;  margin-left: 0.2775em;  display: block;  top: 56px"></span><span class="MathTextBox extra" style="position: absolute;  margin-left: 0.2775em;  display: block;  top: 60px"></span><span class="MathTextBox extra" style="position: absolute;  margin-left: 0.2775em;  display: block;  top: 64px"></span></span><span class="MathRow HBox" style="display: inline-block;  position: relative;  font-size: 15px"><span class="MathMatrix VBox" style="display: inline-block;  position: relative;  text-align: center;  vertical-align: -31px"><span class="HBox" style="display: block;  position: relative;  margin-top: 0px"><span class="VBox" style="display: inline-block;  position: relative;  text-align: left;  vertical-align: 0px"><span class="HBox" style="display: block;  position: relative;  margin-top: 0px"><span class="VBox" style="display: inline-block;  position: relative;  height: 18px;  vertical-align: -6px"></span><span class="MathRow HBox" style="display: inline-block;  position: relative;  font-size: 15px"><span class="MathText MathTextBox text" style="position: relative;  margin-left: 0.05em">x</span><span class="MathRow HBox" style="display: inline-block;  position: relative;  font-size: 15px"><span class="MathText MathTextBox extra1" style="position: relative">(</span><span class="MathText MathTextBox mtext" style="position: relative;  font-style: normal">intcon</span><span class="MathText MathTextBox extra1" style="position: relative">)</span></span><span class="MathText MathTextBox mtext" style="position: relative;  font-style: normal">&nbsp;are&nbsp;integers</span></span><span class="WhiteSpaceBox" style="display: inline-block;  position: relative;  margin-left: 0px"></span></span><span class="HBox" style="display: block;  position: relative;  margin-top: 0px"><span class="VBox" style="display: inline-block;  position: relative;  height: 21px;  vertical-align: -6px"></span><span class="MathRow HBox" style="display: inline-block;  position: relative;  font-size: 15px"><span class="MathText MathTextBox text" style="position: relative;  margin-left: 0.1em">A</span><span class="MathText MathTextBox symbol" style="position: relative;  margin-left: 0.222222em">⋅</span><span class="MathText MathTextBox text" style="position: relative;  margin-left: 0.272222em">x</span><span class="MathText MathTextBox symbol" style="position: relative;  margin-left: 0.277778em">≤</span><span class="MathText MathTextBox text" style="position: relative;  margin-left: 0.277778em">b</span></span><span class="WhiteSpaceBox" style="display: inline-block;  position: relative;  margin-left: 0px"></span></span><span class="HBox" style="display: block;  position: relative;  margin-top: 0px"><span class="VBox" style="display: inline-block;  position: relative;  height: 21px;  vertical-align: -6px"></span><span class="MathRow HBox" style="display: inline-block;  position: relative;  font-size: 15px"><span class="MathText MathTextBox text" style="position: relative;  margin-left: 0.1em">A</span><span class="MathText MathTextBox text" style="position: relative">e</span><span class="MathText MathTextBox text" style="position: relative">q</span><span class="MathText MathTextBox symbol" style="position: relative;  margin-left: 0.222222em">⋅</span><span class="MathText MathTextBox text" style="position: relative;  margin-left: 0.272222em">x</span><span class="MathText MathTextBox symbol" style="position: relative;  margin-left: 0.277778em">=</span><span class="MathText MathTextBox text" style="position: relative;  margin-left: 0.277778em">b</span><span class="MathText MathTextBox text" style="position: relative">e</span><span class="MathText MathTextBox text" style="position: relative">q</span></span><span class="WhiteSpaceBox" style="display: inline-block;  position: relative;  margin-left: 0px"></span></span><span class="HBox" style="display: block;  position: relative;  margin-top: 0px"><span class="VBox" style="display: inline-block;  position: relative;  height: 18px;  vertical-align: -3px"></span><span class="MathRow HBox" style="display: inline-block;  position: relative;  font-size: 15px"><span class="MathText MathTextBox text" style="position: relative">l</span><span class="MathText MathTextBox text" style="position: relative">b</span><span class="MathText MathTextBox symbol" style="position: relative;  margin-left: 0.277778em">≤</span><span class="MathText MathTextBox text" style="position: relative;  margin-left: 0.327778em">x</span><span class="MathText MathTextBox symbol" style="position: relative;  margin-left: 0.277778em">≤</span><span class="MathText MathTextBox text" style="position: relative;  margin-left: 0.277778em">u</span><span class="MathText MathTextBox text" style="position: relative">b</span><span class="MathText MathTextBox symbol" style="position: relative">.</span></span></span></span></span></span></span></span></span></span></span></span></ins></div></td></tr>
</table>
Lilly Schoen
https://wiki.openmod-initiative.org/index.php?title=Mixed_integer_linear_problem&diff=11192&oldid=prev
Lilly Schoen at 08:42, 10 November 2017
2017-11-10T08:42:34Z
<p></p>
<table class='diff diff-contentalign-left'>
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<col class='diff-marker' />
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<td colspan='2' style="background-color: white; color:black;">← Older revision</td>
<td colspan='2' style="background-color: white; color:black;">Revision as of 08:42, 10 November 2017</td>
</tr><tr><td colspan="2" class="diff-lineno">Line 1:</td>
<td colspan="2" class="diff-lineno">Line 1:</td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>{{GlossaryTermTemp</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>{{GlossaryTermTemp</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>|Abbreviation=MILP</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>|Abbreviation=MILP</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">|Definition=A mixed-integer linear program is a problem with</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">- Linear objective function, fTx, where f is a column vector of constants, and x is the column vector of unknowns</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">- Bounds and linear constraints, but no nonlinear constraints (for definitions, see Write Constraints)</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">- Restrictions on some components of x to have integer values</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">In mathematical terms, given vectors f, lb, and ub, matrices A and Aeq, corresponding vectors b and beq, and a set of indices intcon, find a vector x to solve</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">minxfTx subject to x(intcon) are integersA⋅x≤bAeq⋅x=beqlb≤x≤ub</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">|Sources=https://de.mathworks.com/help/optim/ug/mixed-integer-linear-programming-algorithms.html?requestedDomain=www.mathworks.com#btv2z9c</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>}}</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>}}</div></td></tr>
</table>
Lilly Schoen
https://wiki.openmod-initiative.org/index.php?title=Mixed_integer_linear_problem&diff=9719&oldid=prev
Editha Kötter: Created page with "{{GlossaryTermTemp |Abbreviation=MILP }}"
2017-04-20T15:52:20Z
<p>Created page with "{{GlossaryTermTemp |Abbreviation=MILP }}"</p>
<p><b>New page</b></p><div>{{GlossaryTermTemp<br />
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Editha Kötter