All Questions
Tagged with linearization absolute-value
8
questions
0
votes
2
answers
90
views
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
0
answers
65
views
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 ...
- 11
2
votes
1
answer
203
views
Multiple absolute values with multiple variables in an LP
Assume that we have a LP with the constraint
$$ \sum_{j} \left(c_j x_j + |c_j x_j - \alpha_j + \beta_j|\right) \leq y $$
and
$$\alpha_j + \beta_j \leq \lambda_j $$
for all $j$, where the (positive) ...
- 145
6
votes
1
answer
352
views
Absolute value in an equality constraint
What is the best way to model or represent an equality constraint which includes an absolute term in the expression:
$$ x = |y| $$
$x \in \mathbb{R^+}$ and $y \in \mathbb{R}$
- 113
2
votes
1
answer
268
views
How to write constraint with sum of absolutes in Integer Programming?
I found a solution for just one term here
How can we formulate constraints of the form
$$ \sum_{i=1}^n |x_i -a_i| \ge K $$
in Mixed Integer Linear Programming ?
- 203
3
votes
1
answer
1k
views
How to minimize the sum of absolute values
How can I solve a problem such as the following:
$$
\text{minimize}~~~ \sum_{i=1}^n |x_i|
\\
\text{subject to}~~~ A x \geq b
$$
?
Without the absolute values on the variables, it is a simple linear ...
- 1,015
6
votes
1
answer
169
views
Linearizing objective function with absolute differences
I want to turn this objective function
$$\max \sum_{i=1}^{N-1} \sum_{j=i+1}^N |TX_i^T - TX_j^T|$$
where $T$ is just a vector with increasing integers (e.g $[1 \ 2]$) and $X_i$ is a vector ...
- 61
22
votes
3
answers
2k
views
How to minimize an absolute value in the objective of an LP?
I want to solve the following optimization problem
$$\begin{array}{ll} \text{minimize} & | c^\top x |\\ \text{subject to} & A x \leq b\end{array}$$
Without the absolute value, this a ...
- 1,502