Questions tagged [absolute-value]
For questions related to the absolute value function, particularly as it is modeled in optimization problems.
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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 ...
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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
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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 $y \in \mathbb{R}$
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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 ?
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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
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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 ...
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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 ...
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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 ...
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