Questions tagged [linearization]
For questions related to techniques for converting nonlinear expressions in optimization models into equivalent (or approximately equivalent) linear ones.
259
questions
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36
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Add second "constraint" to model a binary variable
in my model I have the binary variable $f_{ij}$ which pushes a time-dependent $j$ integer variable $D_{ij}$ to zero if $f_{ij}$ takes the value 1 and keeps the integer number if $f_{ij}$ equals 0. Yes,...
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1
vote
1
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88
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How to model $\max\limits_{x\in X} \min\limits_{y\in Y} \max\limits_{z\in Z} f(z)$ as single MILP
I have the following optimization problem:
\begin{align*}
\max\limits_{x\in X} &\min\limits_{y\in Y} \max\limits_{z\in Z} & f(z) \\
&\text{such that} & (x, y, z)\in P
\end{align*}
...
- 205
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0
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64
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Is it possible to transform MIQP into MILP without introducing new variable?
I have a QP optimization problem in the form
$$\min {\bf x}^T{\bf Qx}-{\bf c}^T{\bf x}$$
here $\bf Q$ is a symmetric matrix.
$\bf x$ is the optimization variable, and it is binary.
Is there a way to ...
- 2,377
0
votes
2
answers
90
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linearizing a constraint involving an absolute function
I would like to know what is the best way to linearize a constraint involving an absolute function. More precisely, imagine I have three binary variables and their relationships is as follows:
|x-y| = ...
- 97
1
vote
1
answer
89
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Linearizing a quadratic constraint
I am working on a quadratic conic optimization problem, but I have discovered that it would be preferable if the quadratic constraint is linearly approximated. In other words, I need some way to make ...
0
votes
1
answer
59
views
How to linearize this L0 norm of a vector?
I have an QP optimization problem.
$\bf x$ is the binary optimizaion variable of size $12\times 1$.
One of the constraints is non-linear/non-convex.
The constraint is L0 constraint.
The constraint I ...
- 2,377
2
votes
1
answer
216
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How to transform a binary QP into an MILP?
I have a binary quadratic problem with objective ${\bf{x}}^T{\bf{Qx}}+{\bf{c}}^T{\bf{x}}$
subject to
${\bf{A}}{\bf{x}}\le{\bf{b}}$
${\bf{A}}_{eq}{\bf{x}}={\bf{b}}_{eq}$.
here ${\bf{x}}$ is binary.
...
- 2,377
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116
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why this little constraint changes my whole program?
I'm trying to linearize a CP in ILOG CPLEX.
I have the following constraint that I want to linearize (I already simplified it with the big M) :
...
0
votes
0
answers
66
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Why are these two constraint equations not equivalent?
I've made a CP Model of an hospital in ILOG CPLEX and I want to test the performance of the CPLEX version of it.
In my CP model, I have the following constraint :
...
0
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2
answers
126
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Converting a piecewise function to linear equations
I am trying to build a MILP model. In this model, I have a dependent variable (alpha) that its value depends on the value of some other variables (or different combination of some other variables). In ...
- 97
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74
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How to linearize a product of an integer and a binary variable
i have this constraint right here, which is not linear. How would i linearize such a product. $number_t$ is a positive integer and $new_t$ and $reset_t$ are binary.
$$number_t = (number_{t-1}+new_t)\...
- 71
1
vote
1
answer
112
views
Convex approximation of a constraint
I have a constraint given as
$
\left|x_n+\beta x_{n+ 1}\right|-\varepsilon_{ky}\left|x_{n}\right|\leq0\hspace{1em}\forall n=1,2...,N
$ I need to convert this into a convex form to implement in CVX. $...
- 37
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67
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Formulation of a stepwise linear approximation
I am currently trying to solve an MILP in Gurobi. Unfortunately, Gurobi does not support non-linear functions and I would like to do the following. I currently have the following constraint. It ...
- 139
3
votes
2
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232
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Convex equivalent of a constraint
I have a constraint as follows in my MILP model:
$$
\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 ...
0
votes
1
answer
85
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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 ...
- 105