All Questions
Tagged with linearization linear-programming
94
questions
0
votes
1
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75
views
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
2
votes
2
answers
184
views
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
2
votes
1
answer
78
views
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:
$$
l, m, n \...
- 1,857
2
votes
1
answer
223
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Set a limit on value change of a binary variable
I am working on an Energy Management problem. The objective is to minimize the electricity bill for the customer.
I have a time-series data with 15 min. intervals spanning the course of 1 year. The ...
2
votes
1
answer
126
views
How to model the constraints of min and max in cvxpy
I have a continuous variable $x_{ij}\in[0,1]$ and I need to write the following constraint:
$$M_i-m_i+1\leq C_i$$ where $M_i=\max\{j: x_{ij}>0\}$ and $m_i=\min\{j: x_{ij}>0\}$
- 403
4
votes
2
answers
309
views
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?
- 41
0
votes
1
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105
views
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
votes
1
answer
194
views
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 ...
1
vote
1
answer
45
views
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 (...
- 97
1
vote
1
answer
88
views
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
1
vote
1
answer
89
views
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
2
answers
126
views
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
-1
votes
1
answer
74
views
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
2
votes
1
answer
251
views
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
1
answer
141
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 $i$. ...