New answers tagged optimization
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Ways to improve lower bounds while solving MIPs
There are serveral strategies.
I recomend Lagrangian and Surrogate relaxation.
Look for James Davis video "2.6 lagrangian relaxation". I guess it would help.
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Accepted
MIP formulation for a lower semi-continuous function
You want to maximize $\max(f(x),0)$. Assume $L \le f(x) \le U$ for constants $L$ and $U$. Maximize $g(x)$ subject to
$$
0 \le g(x) \le U y \\
0 \le g(x) - f(x) \le (0-L)(1-y) \\
y \in \{0,1\}
$$
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Maximizing sum of probabilities with variable distributions
One possible way to do what you want is through the use of chance constraints, which are used to constrain probabilities to be greater than or less than some value. I'm not familiar with a Skellam ...
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Job Scheduling with Energy Consumption using Linear Programming
Using this link (kind of constraint programming), lets define $ s_{j}$ as start time for task $j$ over a domain of $ T =\{1,2,...720 \}$ mins on core $c$ with $d_j$ being the processing time for a ...
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How to design a constraint to control flow in a non-network optimization model
I actually solved this problem recently on my own, though my approach was not based entirely on operations research, but relied a bit on the logic of running the whole program. So if you are looking ...
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Accepted
How to design a constraint to control flow in a non-network optimization model
Ok, suppose production process $i1$ goes to consumption process $ i2$. You can create a map of $ i1 -> i2$ & define parameters $z_{i1,i2}$such that if $ i1 -> i2$, then $ z_{i1,i2} = 1$, $0$ ...
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Algorithms to use for an assignment problem
Say you've a set of sewing lines $ L = \{l_1,l_2,...l_5 \}$.
At the beginning of the week you have a set of orders $O$, a set of styles $S$ & for each style $s$ a set of lines in descending order ...
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Algorithms to use for an assignment problem
You can approach this problem using either a mixed-integer linear program (MILP) or a constraint programming (CP) model (using a CP solver that supports global constraints designed for scheduling ...
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What kind of optimization problems are solved most often in practice?
Manufacturing applications based on tailored versions of Product-Mix Optimization and Diet Problem Optimization are also used a lot, daily.
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What kind of optimization problems are solved most often in practice?
Look at case studies from LocalSolver:
https://www.localsolver.com/docs/last/exampletour/index.html
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Optimization algorithm for space debris
ACO, genetic algorithms and other metaheuristics can be adapted to constrained problems by adding to the objective function penalties for constraint violations and then treating the problem as ...
- 37.8k
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How do you get the primal solution of an LP from the dual solution?
If in primal problem the variable $\mathbf x$ was a vector of dimension $n$ and constraints were made of $m+p$ equations, in dual problem we should have $n$ equations in $m+p$ variables.
It is common ...
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Constrained optimization of a sum
The problem
$$
\begin{array}{rcl}
\min & \sum_{j=1}^n c_j x_j & \\
\mbox{st} & \sum_{j=1}^n x_j & = & b, \\
& l \leq x \leq u. & & \\
\end{array}
$$
can ...
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Constrained optimization of a sum
Primal Problem
$$\begin{align}
\text{maximize} \quad & \sum_{i=1}^n c_i x_i \\\
\text{subject to} \quad & \sum_{i=1}^n x_i = 0 \\
& x_i \ge -1 \quad \forall i=1,\ldots,n \\
& x_i \le ...
- 365
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What is the benefit of developing opensource git-respository for the developer?
Another obvious benefit is that users will try many configurations and ideas, find possible bugs, thus making the library more robust.
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Convex approximation of an expression with fraction for CVX
I assume the given problem is
$$
\max \frac{\|ax-b\|^2}{\|cx+b\|^2}, x \in \mathbb{C}^N
$$
I may try the following relaxation. The given problem is equivalent to
$$
\begin{align}
&\max &\|ax-...
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votes
Convex approximation of an expression
No approximation is needed if you wish to minimize the expression. For maximization, see the material after "Edit".
Due to cyclic permutation invariance of trace,
$$\text{trace}(X) = \text{...
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