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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Linearization of two constraints: one with a conditional max and one with a sum with a variable as index
I have these two quite nasty constraints I have tried to linearize. I am trying to dynamically control if you are allowed to plan producing product p. You are allowed to do it if the product arrived (...
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What's the linearization of the product between a discrete variable and a continuous varibale?
I am trying to linearize the product $z=xy$, where $x$ is an integer variable and $y$ a continuous variable, both non-negative, for an optimization problem. I have tried the SCIP formulation:
$v_{bn} \...
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How to write conditional constraints and sum the result in Linear Programming in Python?
I want to use the sum of a series of linear expressions as objective and constraints. These linear expressions are chosen to be included or not based on some conditions. I can achieve it in Excel ...
- 13
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PULP: Optimization Assignment of Bicycle production per month
Q1. If bicycles of types A and H are produced, then bicycles of type C can be produced with 20% shorter working hours, while selling profit of bicycles type H can be 20% higher.
Q2: If bicycles of ...
3
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199
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How to linearize the following logical constraints?
I am having trouble linearizing the following logical constraints.
$x,y,z$ are non negative continuous variables such that $x=y+z$, and $A$ is a positive parameter. I would like to linearize
$$
y=
\...
- 79
2
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2
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184
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Are McCormick Envelopes exact for the following class of optimization problems?
I have the following optimization problem:
\begin{align*}
\text{minimize} \quad &\mathbf{c^T x} \\
\text{such that} \quad &\mathbf{x} \in S.
\end{align*}
Here, $S$ is a polyhedron of the form $...
- 205
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78
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Minimizing sum(abs(Ax-c)) for binary decision variables - terminology and methods?
My problem requires choosing a fixed number of vectors from a large set of vectors such that the sum of these vectors is close to some known target vector. That is, given known parameters:
$$
l, m, n \...
- 1,857
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223
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Set a limit on value change of a binary variable
I am working on an Energy Management problem. The objective is to minimize the electricity bill for the customer.
I have a time-series data with 15 min. intervals spanning the course of 1 year. The ...
2
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1
answer
139
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Priority based demand fulfilment in Linear Constraint
Say I have 3 sources. D1, D2, D3. their capacity is 100, 200, 400. I want to create some constraints such that First D1 is depleted then D2 and then D3. But the catch is you cant use min or max ...
2
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126
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How to model the constraints of min and max in cvxpy
I have a continuous variable $x_{ij}\in[0,1]$ and I need to write the following constraint:
$$M_i-m_i+1\leq C_i$$ where $M_i=\max\{j: x_{ij}>0\}$ and $m_i=\min\{j: x_{ij}>0\}$
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309
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Linear condition between two continuous variables
There are two real variables $x$ and $y$. The conditions are such that:
if $y\le 0$, then $x=0$
if $y>0$, then $x=y$
How to write linear equations or inequalities to satisfy both the conditions?
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How to model this constraint in a better way?
I have a resource allocation problem. There are $M$ users and $N$ resources (machines).
One user can be assigned to multiple resources/machines.
But maximum $B$ machines can be activated at a time for ...
- 2,377
3
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194
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Reformulate constraints
I have the following constraints and am wondering whether I can formulate the whole thing more narrowly and with fewer constraints. $x_{itk}$ is binary and $u_{it}, v_{itk}\in [0,1]$. $M$ is a Big-M ...
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Is the linearization with first-order Taylor approximation correct?
I have a QP problem as
$\min \hspace{2mm} x^TQx-c^Tx$
here $x$ in binary
I want to transform it into a MILP by writing the objective function as
$\min \hspace{2mm} z-c^Tx$
and then adding a constraint
...
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Converting a function composing of multipe pieces into a linear equation
I have a variable (alpha) which depends on some other binary variables, denoted as X_i. So, for some combination of other variables, alpha may take a value (Beta_j). I added some auxillary variables (...
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