Questions tagged [indicator-constraints]

For questions on constraints controlled by binary variables.

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When to use indicator constraints versus big-M approaches in solving (mixed-)integer programs

Various optimization modeling languages and solvers allow for both indicator constraints (see for example here, here and here) and traditional binary variable and big-M approaches can be used to model ...
• 193
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Mocking up conditional statements in LP

I would like to know how if condition statements in linear programming can be reformulated using indicator constraints, and hence solved as a mixed integer linear program. Specifically: 1. Is it ...
• 161
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Piecewise function with two variables

I have a square like region centered at the origin, which is divided into 4 sub-regions. Region 1 can formed from by the diagonal of a square, $x + y \leq 0$. Region 2 is formed by joining the center ...
• 153
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Logical equivalencies to modeling an indicator decision variable in transportation problem

I am formulating a model that seeks to minimize the cost of shipping goods from factories to warehouses, where the cost of shipping is independent of the type or amount of goods being shipped (except ...
• 271
470 views

Portfolio optimization with indicator function constraint in CVXPY

I have the following portfolio optimization problem that I want to solve using CVXPY: \begin{align}\min_w&\quad w^\top\Pi\\\text{s.t.}&\quad\sum_{i=1}^nw_i=1\\&\quad w^\top\Sigma w\le\...
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Indicator function for integer variable with inequality constraint

I have $n$ integer variables $\vec{x}$ with the following integer programming problem. $$COST = \sum^{n-1}_{i = 0} a_i x_i + \sum^{n-1}_{j=0} b_j I(x_j > 0)$$ Here, $a_i, b_j \in \mathbb{R}_+$ ...
• 251
1 vote
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Matrix lookup modelling variants

As part of a bigger model I have a matrix of variables $x_{ij} \geq 0$ and a "selector" set of variables $y_j \in \{0,1\}, \sum_j y_j = 1$. From $x_{ij}$ I'd like to get the variables of ...
• 113
1 vote
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if else condition with multiple criteria in MIP

I have problem like below Decision variable x1 >= 0 But it depends on selection variable s1 as binary variable If s1 = 0 then x1= 0 and if s1 = 1 then x1>0 how I can write this as constraint for ...
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1 vote
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1 vote
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How to model this chain of logical implication

I would like to seek some advice on modeling the following (chain of) logical implication: For instance $\omega_{xy}$ might indicate precedence, i.e., $x$, $y$ being the nodes $x$ and $y$, ...
• 707
1 vote
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Assistance in formulating implication constraints for inequalities

I would like to seek some advice on modeling the following logical implications, where $\delta$ is a binary variable, $D_{j}$ and $A_{j}$ are nonnegative discrete variables, and $p_{j}$ are ...
• 707
1 vote
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Mixed Integer programming, the big M

In the constraints below, why have they used the big M? What do we look for in order to identify the big M in other questions?
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1 vote