# Questions tagged [linearization]

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

116 questions
Filter by
Sorted by
Tagged with
113 views

### Alternate formulation for modeling inventory constraints

I'm working on a inventory optimization problem where inventory used at a time-period is computed based on price-bucket that is selected for an item. Problem contains multiple items (around 10K), 15-...
410 views

### How to linearize a constraint with a maximum of a linear function

I want to linearize the following statement into a MILP: $\forall x\in \mathbb{R}^{m}$ satisfying $Cx \le d$, $\exists i\in \{1,\cdots,m\}$ such that $a_i^Tx \ge b_i$, where $a_i$ and $b_i$ are given ...
359 views

### How to model this expression?

Suppose $0\le x \le 1$ is a decision variable and $\gamma(x)$ is defined as follows: $$\gamma(x)= \begin{cases} \theta & x>0\\ 0 & x=0 \end{cases}$$ where $0\le \theta\le 1$. In my model, ...
123 views

### Linearise $\max\{ y_{t-1} + a_t - z_t ,0\}$

I'm trying to linearise these constraints, but I am not able to do correctly do it. $$y_t = \max\{ y_{t-1} + a_t - z_t, 0 \}$$ My attempt was this: \begin{align}y'_t &\geq a_t - z_t\\y'_t &\...
127 views

116 views

### Maximizing a piecewise-linear convex function

Note: Initially posted on MathOverflow. I am working on an optimization problem where some of the terms of the objective function to maximize are expressed as a piecewise linear function of variables:...
85 views

### How to linearise this nonlinear constraint?

I have a constraint in the form $\sum_{n=1}^{N}x_{m,n}\omega_{m,n}\ge (t_u-1)\beta_u, \forall u, u=1,2,\cdots, U$ where $x_{m,n}$ is binary variable $t_u$ and $\beta_u$ are continuous optimization ...
130 views

234 views

### How to linearize the Min function while letting the binary variable to be fixed for x1==x2 as well?

As discussed here, the min function, i.e $X = \min\{x_1,x_2\}$, can be linearized as follows: \begin{align} X & \le x_1 \\ X & \le x_2 \\ X & \ge x_1 - ...
101 views

### 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 ...
154 views

### Linearize sum of continuous and boolean variable

For maximizing the objective function $\sum_i{d_i y_i}+ A x - B \cdot \mathbb{I}_{x>0}$, how can I linearize $A x - B \cdot \mathbb{I}_{x>0}$ term where $d_i, A$ and $B$ are positive constants ...
166 views

### Strong MIP formulations for a large-scale mixed-integer nonlinear feasibility problem

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 ...
132 views