Linked Questions

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} ...

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 ...

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 ...

For continuous variables $x$ and $y$, the constraints are: ...

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 \ \ \...

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\...

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 ...

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 ...

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 ...

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 ...

This is my first real optimisation 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\...

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 ...

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 $y$, ...