Linked Questions

4 votes
0 answers
116 views

Conditional constraint formulation [duplicate]

How can I create constraints to make sure $x=1$ if $k\geq 0$ and $x=0$ if $k<0$, where $x\in \{0,1\}$ and $k\in \mathbb{R}$? Here is my attempt: \begin{equation}\label{cons:1} \begin{aligned} ...
tcokyasar's user avatar
  • 1,249
32 votes
3 answers
19k views

In an integer program, how I can force a binary variable to equal 1 if some condition holds?

Suppose we have a binary or continuous variable $x$, a binary variable $y$, and a constant $b$, and we want to enforce a relationship like If $x \gtreqless b$, then $y = 1$. How can we write this ...
LarrySnyder610's user avatar
15 votes
4 answers
2k views

Single reference for Mixed Integer Programming formulations to linearize, handle logical constraints and disjunctive constraints, do Big M, etc?

Is there a single crisp and accessible reference which covers how to generate Mixed Integer Programming formulations to linearize products, handle logical constraints and disjunctive constraints, do ...
Mark L. Stone's user avatar
12 votes
1 answer
5k views

If-then constraints in MIP programming

For continuous variables $x$ and $y$, the constraints are: ...
Qbik's user avatar
  • 221
13 votes
1 answer
924 views

Representing an indicator function: binary variables and "indicator constraints"

I want to represent the indicator function: $$ \mathbb{1}_{(y=j)}$$ where $y$ is a non negative, integer variable. My attempt is as follows: define a binary variable: $$ z_j =\begin{cases} 1 \qquad\...
Libra's user avatar
  • 937
4 votes
2 answers
299 views

Conditional Constraint in MIP

I need to formulate a conditional constraint for a binary variable z defined as: $z_{i,j,k}$, $\ \ i=1:10 \ , \ j=1:5 \ , \ k=1:3$ If any $z_{i,j,3} = 1$ then $z_{i,j,1} + z_{i,j,2} = 0 \ \ \...
Psyndrom Ventura's user avatar
3 votes
2 answers
505 views

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 ...
Sam's user avatar
  • 161
2 votes
1 answer
628 views

Same values constraint and grouping of variables

In a linear program, I would like some variables to: 1. Take the same values 2. Group some variables i.e. some variables should take same values or lie within certain percentage. 3. All different ...
Sam's user avatar
  • 161
3 votes
1 answer
309 views

Linearizing constraint with continuous and boolean variables

I have two continuous variables $A$, $B$ and two binary variables $x$, $y$. Condition: if $A = B \wedge x = 1 \wedge y=1$ then $z = 1$ else $z = 0$ from In an integer program, how I can force a ...
ooo's user avatar
  • 1,589
5 votes
2 answers
104 views

How to formulate case distinctions in AMPLs objective function?

This is my first real optimization problem I formulated and now trying to solve by using AMPL. The following objective function is from a linear 0-1 LP means all variables $x_i^b\in\{0,1\}$, with $i\...
baxbear's user avatar
  • 319
2 votes
1 answer
196 views

How to transform these conditional constraints to linear integer ones in a more efficient way?

The conditional constraints A and B can be transformed to a set of linear integer constraints as follows: A) $\text{if} \ x_1=0 \ \text{then} \ d_1=1 \ \text{else} \ d_1= 0\\ x_1\in {\rm I\!R}^{\geq ...
SAH's user avatar
  • 294
1 vote
1 answer
149 views

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 $y$, ...
Mike's user avatar
  • 717
3 votes
1 answer
161 views

How to optimize with "if" constraints

The minimizing problem is the following : $$ \underset{w}{\operatorname{argmin}} \sum_{i=1}^{n}\left[w_{i}\times (\frac{Vw}{\sigma})_{i} - b_{i}\right]^{2}$$ with $V$ a $n\times n$ matrix (covariance ...
FredNgu's user avatar
  • 157