Linked Questions

0 votes
0 answers
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Linearizing max constraint Problem [duplicate]

I want to linearize a max constraint as below: In which x_(i,t),are binary decision variables and T is a constant. How can I linearize this constraint?
Yousef Mirzaeian's user avatar
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
25 votes
2 answers
6k views

Why is it important to choose big-M carefully and what are the consequences of doing it badly?

The question here discusses the two different use of "big-M method", where one of them is the big-M in logical constraints and linearization in (mixed-)integer programming problems (that's what I'm ...
EhsanK's user avatar
  • 5,874
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
22 votes
3 answers
2k views

How to minimize an absolute value in the objective of an LP?

I want to solve the following optimization problem $$\begin{array}{ll} \text{minimize} & | c^\top x |\\ \text{subject to} & A x \leq b\end{array}$$ Without the absolute value, this a ...
Discrete lizard's user avatar
11 votes
4 answers
989 views

How to linearize a constraint with a maximum of binary variables times some coefficient in the right-hand-side

I have the following constraint that I'd like to linearize: $P$ is a given set $b_p \in \{0,1\} , \forall p \in P$ a binary variable associated with each element of $P$ $c_p \in \mathbb{R}^+$, a ...
Renaud M.'s user avatar
  • 2,418
7 votes
1 answer
10k views

How to linearize min function as a constraint?

I'm trying to solve an optimization problem including following constraint, and I need to linearize it in a maximization nonlinear programming model. Please help me to reformulate it with mixed ...
Vida's user avatar
  • 87
8 votes
2 answers
3k views

How to linearize a constraint with max

I would like to linearize a constraint with max. I have the following constraint: $$\max_{pcj}X_{pwcj}\leqslant L_{wk}.$$ With this constraint, I would like to ensure that for $\forall w \in W$, no ...
campioni's user avatar
  • 1,133
10 votes
1 answer
1k views

Linear programming with if-then-else (big-M)

I am trying to formulate the following in linear programming. \begin{cases}\text{if}\,\,a>b\,\,\text{then}\,\,c=a\\\text{else}\,\,c=b.\end{cases} I tried some things with big $M$, like $$a + my &...
Harry van t Kamp's user avatar
10 votes
2 answers
407 views

Use integer/quadratic programming to maximize consecutive zeros in a binary array

A binary array $t = [t_1, t_2, t_3, t_4, t_5]$ with each element a binary integer variable taking values 0 or 1. You can think this vector as slots with 1 representing the slot being taken and 0 ...
MIMIGA's user avatar
  • 201
6 votes
1 answer
518 views

Convert summation of min functions into linear constraints for optimization

I have the following optimization problem: $$ \mbox{maximize } j^{*} \mbox{ subject to:} \sum_{j^{*}\leq j\leq J} \min({\bf A}_j,{\bf B}_j) \geq \lambda, \lambda \in \mathbb{R} \mbox{ and } {\bf A}_j,{...
jackson95's user avatar
6 votes
1 answer
292 views

How To Linearize $X = \max\{x_1,x_2\}$

I am new to thinking about math programming and I have a particular constraint I am hoping to reformulate, I just don't know the proper mathematical translation for what I am hoping to do. Enforcing ...
GrayLiterature's user avatar
6 votes
1 answer
169 views

Linearizing objective function with absolute differences

I want to turn this objective function $$\max \sum_{i=1}^{N-1} \sum_{j=i+1}^N |TX_i^T - TX_j^T|$$ where $T$ is just a vector with increasing integers (e.g $[1 \ 2]$) and $X_i$ is a vector ...
T K.'s user avatar
  • 61
3 votes
1 answer
99 views

defining Mixed integer linear inequalities for a set of variables

The problem is described as follows: considering $n$ variables which are continuous and bounded such that $$L_i \le x_i \le U_i\quad \forall i=1,2,\dots,n.$$ How can i define a set of mixed integer ...
george's user avatar
  • 135