Questions tagged [linearization]
For questions related to techniques for converting nonlinear expressions in optimization models into equivalent (or approximately equivalent) linear ones.
259
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How to linearize stepped pricing in a route assignment problem
There is an allocation problem, while we have to assign logistics routes to multiple candidate carriers.
For simplicity, let's assume there are only two routes, $A$ and $B$, with two candidate ...
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435
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Is it possible to do a linearization without introducing new variables?
I have three binary variables $x_{i,j}^{m,r}$ , $y_i^{m,r}$, and $z_i^{m,r}$. There is another integer variable $w_i^r$. And I want to linearize the following logic:
$$ \sum_{m} x_{i,j}^{m,r} \ge 1 \...
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applying a piecewise linearized equation in pulp
The background is I'm building a toy rent vs. buy mortgage calculator. I am an experienced software engineer but my math skills are 20 years behind me and I admit to being very lost.
I've been using ...
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Linearizing if else conditions in ILP
We are given three binary indicator variables $X_{ij}, Y_{jk}$ and $Z_{jl}$. Write linear constraints such that,
a) if $X_{ij}$ is equal to 1, then for that $j$ when $X_{ij} = 1$, exactly one $Y_{jk} =...
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Transforming a quadratic constraint into a linear constraint
I have a problem with a quadratic constraint and I want to transform it into a linear constraint. This would help to reduce the computational time of my problem.
Following constraint should be ...
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Linearization of Conditional Constraints for MIP using Cplex
I'm currently working on a mixed-integer programming (MIP) problem and I'm trying to implement a set of conditional constraints in CPlex. These constraints involve decision variables that are indexed ...
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77
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Optimize revenue function with log part
I am working on an optimization problem where I aim to maximize revenue. My current model has the following objective function:
$$ Sales(P_i) * log(P_i - const_i))$$ where $P_i$ represents the price ...
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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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How to linearize the multiplication of variables and transform this into an MILP?
Let $C=10$, $U=50$
$P_c,c=1,\cdots,C$ and $\alpha_{u,c},u=1,\cdots,U,c=1,\cdots,C$ are optimization variables
$\alpha_{u,c}$ is binary
$\sigma_{u,c}$, $d_{u,c}$ are known parameters
$\min \sum_{c=1}^...
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How to linearize the multiplication by a binary decision variable?
I am currently optimizing a hydrogen production chain.
I am optimizing the production regime, and the size of the required wind, solar and the electrolyser.
For every hour of the year, the production ...
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198
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Non-Linear objective function due to piecewise component
I have the following objective function:
$\sum_{n}(1-prob_{n})(1+x_n)$
Where $x$ is my decision variable. $prob_{n}$ is a piecewise function that can look like:
$prob_{n} = $
\begin{cases}
0.5, ...
- 67
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3
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358
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Systematic references on linearizing conditional / logical expressions
On this site, one can usually finds questions like “How to transform my expression into linear form?” The expressions usually contain and, ...
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Interpret the formulation of a pricing model in crowdshipping
I am trying to run the pricing model from the paper "Designing pricing and compensation schemes by integrating matching and routing models for crowd-shipping systems" on python with Gurobi, ...
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How to show that minimizing the epsilon-insensitive loss is equivalent to a quadratic program with inequality constraints?
This question is about an optimization problem that arises in support vector regression (SVR). Suppose you have $N$ pairs $(\vec{x}_n, y_n)$ as data and would like to find a vector of weights $\vec w \...
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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?
