# 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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### Formulation of a stepwise linear approximation

I am currently trying to solve an MILP in Gurobi. Unfortunately, Gurobi does not support non-linear functions and I would like to do the following. I currently have the following constraint. It ...
234 views

### Convex equivalent of a constraint

I have a constraint as follows in my MILP model: $$\sum_{e} (a_1(e) - a_2(e))^2 \leq M$$ Where, $a_1(e)$ and $a_2(e)$ are binary variables. Would you please guide me how can I find the equivalent ...
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### How to represent "if $y_{it} = 1$ and $z_{jt'}=1$ then $x_{ij,t+t'}=1$"

There is a fulfillment problem in the e-commerce logistics field, where the fulfillment of each order is composed of a main transport (from City A to City B, referred to as a route) and an end ...
• 115
59 views

### Better formulation of bilinear terms

I am working on an optimization problem where I need to formulate a constraint that represents the total sales value under specific conditions. The challenge lies in creating an expression that ...
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### Replace the constraint using ==> by a linear formulation

I would like to know how to express the continuity constraint without using a decision variable in the conditional form. My challenge is to stay with a linear formulation. I will start to explain my ...
1 vote
143 views

### How do I linearize such a constraint?

I was wondering, how one would linearize such a constraint, to make it applicable to LPs. $a_{i}=(a_{i-1}+b_{i})(1-c_{i})-d_{i}$ $a_i$ gives information of the number of assigned jobs to machine $i$. ...
99 views

### How to transfer an objective with separate positive and negative parts into linear programming

I've got to deal with an optimization problem as follows, \begin{aligned} \max_{x,y} & a^Tx+y^TKx\\ {s.t.}&Ax=b\\ &{Cx}\leq d\\ l&\leq y\leq u\end{aligned} where $x \in \bf{R}^n$,...
330 views

### Optimization problem with the Harmonic number

I have an optimization problem: \begin{align*} \text{ minimize } \sum_{i=1}^n H(x_i) \\ \text{ subject to } Ax \geq b, x\geq 0, x\in \mathbb{Z}^n \end{align*} where $H(n)$ is the $n$-th Harmonic ...
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1 vote
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### Moment based linearization of PDF for LP based optimization

Suppose I’m interested in modeling risk/volatility using the Cauchy distribution and I’d like to optimize some allocations using linear programming. The Cauchy distribution is quadratic in nature but ...
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1 vote
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### transform minimize weighted sum of absolute value into a linear optimization

For example, we have an optimization problem $$\min \sum_{i=1}^{n} |w_{i} - a_{i}| b_{i} \quad \text{s.t.} \quad \sum_{i=1}^{n} c_i w_i = 0$$ and $a_i, b_i, c_i$ are given. How to convert it into a ...
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1 vote
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• 113
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