# 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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### 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 ...
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 ...
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 ...
1 vote
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### Transforming a quadratic constraint into a linear constraint

I have a problem with a quadratic constraint and I want to transform it into a linear constraint. This would help to reduce the computational time of my problem. Following constraint should be ...
1 vote
68 views

### Linearization of Conditional Constraints for MIP using Cplex

I'm currently working on a mixed-integer programming (MIP) problem and I'm trying to implement a set of conditional constraints in CPlex. These constraints involve decision variables that are indexed ...
76 views

### Optimize revenue function with log part

I am working on an optimization problem where I aim to maximize revenue. My current model has the following objective function: $$Sales(P_i) * log(P_i - const_i))$$ where $P_i$ represents the price ...
95 views

### Representing a Multi-Level Categorical Variable using Big-M Method in Linear programming

I'm working with a statistical linear model where I have a variable, ( N ), representing the percentage of charging of a battery. Based on ( N ), I derive another variable, ...
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### using milp for a linear complementarity problem

I have to minimize $c^Tx$ subject to $Ax = b$, $x_iw_i = 0$ for all $i$, with $x$ non negative continuous and $w$ binary. What model should I use to solve this problem?
1 vote
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1 vote
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### Nonlinear fractional objective function

Could you please teach me when an optimization model with fractional terms in the objective function can be linearized or solved optimally? I only know that if the objective function has a single ...
236 views

### Linearizing a disjunctive expression into MILP

I want to linearize the following disjunctive form. $$\left[\begin{gathered}w_{1}\\x \geq a\end{gathered}\right] \vee \left[\begin{gathered}w_{2}\\x \geq b\end{gathered}\right]$$ where $w_1$ and $w_2$...
323 views

### How to deal this L0 norm of a vector of L2 or L1 norms in objective?

I have an optimization variable denoted as ${\bf A\in\mathbb{C}^{100\times 5}}=[{\bf a}_1\hspace{1mm} {\bf a}_2 \hspace{1mm} {\bf a}_3 \hspace{1mm} {\bf a}_4 \hspace{1mm} {\bf a}_5];$ Here, ${\bf a}_1$...
39 views

### Choosing upper and lower bound using big-M [duplicate]

This question is related to my previous question posted here: Piecewise constraint using big-M notation and this question posted on the math stackexchange: https://math.stackexchange.com/questions/...
How can I linearize this constraint $$d_{u,c}\sigma \le \|{\bf f}_{u,c}\|^2\le Td_{u,c}$$ $\sigma$ is a very small number based on scale of $f$ $T>0$, ${\bf f}_{u,c}$ is optimization variable, a ...
I would like to linearize a product, for example $a*b$. if I solve my solution in log space, I can formulate it as $a+b$ and when my final output is returned, remember to convert back to original ...