Questions tagged [absolute-value]
For questions related to the absolute value function, particularly as it is modeled in optimization problems.
4
questions
3
votes
1
answer
159
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 ...
6
votes
1
answer
112
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
20
votes
3
answers
634
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 ...
- 1,462
17
votes
1
answer
931
views
Working with absolute values in constraint in a LP or MILP
Having all the approaches explained in the blog called "OR in an OB World" (this address) in my mind, I would like to ask the following question:
What is the best practice to make a constraint linear ...
- 8,340