# Questions tagged [linearization]

For questions related to techniques for converting nonlinear expressions in optimization models into equivalent (or approximately equivalent) linear ones.

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### How to linearize membership in a finite set

Given finite set $S$ and variable $x$, how do I linearize the set membership constraint $x\in S$?
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### Model “if and only if” indicator constraints in Linear programming

Apologies if this question has been asked, but I haven't been able to find it. I'm modelling something with Gurobi and want to do the following: \begin{align}\text{cond} < \dfrac{1}{3} &\iff x =...
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### Linearization of a quadratic model, what is the difference while using gurobi?

I have a quadratic model of parking $N$ cars in $S$ separate lanes as follows. Each car has an arrival time and a departure time. Departure follow the last in first out principle. The objective is to ...
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### Problems modeling a constraint in network design problem

I'm working on a network design problem where the objective is to minimise the network design cost. Given a graph G = (V, E) and a set of point-to-point demands K, the task is to route the demands and ...
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### What is a good way to penalise LP relaxation?

I have a binary integer program. It is of a large size and the solver is taking longer time. I am thinking of relaxing the binary integer variable and making it a continuous variable. How can I ...
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### Forbid transformation of max(x,y) into MILP

The function $\max(x,y)$ can be linearized by making use of additional binary variables. I suppose global optimisers are implemented to perform this transformation automatically. Is there a global ...
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### Linearize a product of binary variables

I have a function to minimize which has the following term $$\sum_{i\in I}\sum_{j\in J}\sum_{k\in K}x_{ijk}N_{ij}a_{ijk},$$ where the variables are $x_{ijk}\in\{0,1\}$, $a_{ijk}$ are given as input ...
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### Formulating these logical constraint in an ILP

I have these two constraints : $z \leq My$ $t \leq M'y$ where $z$ and $t$ are two integer variables $z, t\geq 0$, $y$ is a binary variable, and $M$, $M'$ are two big numbers. So basically these ...
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### Sensible and realistic way to model truck based transport costs depending on amount

Different kinds of problems involve transporting an amount $x$ from A to B which results in a cost $c(x)$ in the objective function. Traditionally, often linearized costs are used to get an easy, ...
I'm trying to construct a strong MIP formulation for the following integer nonlinear feasibility problem. Informally: We have a $m \times n$ decision matrix of binary variables Each row of the matrix ...