Mixed integer linear problem

Revision as of 08:54, 10 November 2017

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.

Abbreviation

MILP

Synonyms

Superterms

Subterms

Sources

https://de.mathworks.com/help/optim/ug/mixed-integer-linear-programming-algorithms.html?requestedDomain=www.mathworks.com#btv2z9c

minxfTx subject to {x(intcon) are integersA⋅x≤bAeq⋅x=beqlb≤x≤ub.

@@ Line 12: / Line 12: @@
 |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">&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>
+<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><br/>

About

Help

Search

Navigation

Search

Interaction

Toolbox

Namespaces

Variants

Views

Actions

Mixed integer linear problem

Revision as of 08:54, 10 November 2017

Contents

Definition

Abbreviation

Synonyms

Superterms

Subterms

Sources

Log in / create account

About

Help

Search

Navigation

Search

Interaction

Toolbox

Namespaces

Variants

Views

Actions

Mixed integer linear problem

Revision as of 08:54, 10 November 2017

Contents

Definition

Abbreviation

Synonyms

Superterms

Subterms

Sources