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| | {{GlossaryTermTemp | | {{GlossaryTermTemp |
| | |Abbreviation=MILP | | |Abbreviation=MILP |
| | + | |Definition=A mixed-integer linear program is a problem with |
| | + | |
| | + | - linear objective function, fTx, where f is a column vector of constants, and x is the column vector of unknowns |
| | + | |
| | + | - bounds and linear constraints, but no nonlinear constraints (for definitions, see Write Constraints) |
| | + | |
| | + | - restrictions on some components of x to have integer values |
| | + | |
| | + | 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. |
| | + | |Sources=https://de.mathworks.com/help/optim/ug/mixed-integer-linear-programming-algorithms.html?requestedDomain=www.mathworks.com#btv2z9c |
| | }} | | }} |
| | + | <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"> subject 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"> are 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><br/> |
Latest revision as of 08:54, 10 November 2017
[edit] Definition
A mixed-integer linear program is a problem with
- linear objective function, fTx, where f is a column vector of constants, and x is the column vector of unknowns
- bounds and linear constraints, but no nonlinear constraints (for definitions, see Write Constraints)
- restrictions on some components of x to have integer values
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.
[edit] Abbreviation
MILP
[edit] Synonyms
[edit] Superterms
[edit] Subterms
[edit] Sources
https://de.mathworks.com/help/optim/ug/mixed-integer-linear-programming-algorithms.html?requestedDomain=www.mathworks.com#btv2z9c
minxfTx subject to {xintcon are integersA⋅x≤bAeq⋅x=beqlb≤x≤ub.
