6
votes
Accepted
Gurobipy MILP model comes infeasible yet can't compute IIS because "the model is feasible"
This model is likely on the borderline between feasibility and infeasibility. The algorithm used to determine feasibility in the solver is different than the algorithm used in IIS, and may reach a ...
- 13.1k
2
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,
$$\text{trace}(X) = \text{...
- 13.1k
2
votes
Constrained optimization of a sum
The problem
$$
\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}
$$
can ...
- 3,046
2
votes
Accepted
MIP formulation for a lower semi-continuous function
You want to maximize $\max(f(x),0)$. Assume $L \le f(x) \le U$ for constants $L$ and $U$. Maximize $g(x)$ subject to
$$
0 \le g(x) \le U y \\
0 \le g(x) - f(x) \le (0-L)(1-y) \\
y \in \{0,1\}
$$
- 30.4k
1
vote
Accepted
How to design a constraint to control flow in a non-network optimization model
Ok, suppose production process $i1$ goes to consumption process $ i2$. You can create a map of $ i1 -> i2$ & define parameters $z_{i1,i2}$such that if $ i1 -> i2$, then $ z_{i1,i2} = 1$, $0$ ...
- 3,343
1
vote
Optimization algorithm for space debris
ACO, genetic algorithms and other metaheuristics can be adapted to constrained problems by adding to the objective function penalties for constraint violations and then treating the problem as ...
- 37.8k
1
vote
What is the benefit of developing opensource git-respository for the developer?
Another obvious benefit is that users will try many configurations and ideas, find possible bugs, thus making the library more robust.
- 12.9k
1
vote
Convex approximation of an expression with fraction for CVX
I assume the given problem is
$$
\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-...
- 1,036
1
vote
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
1
vote
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
- 141
Only top scored, non community-wiki answers of a minimum length are eligible