5
votes
Accepted
Which MiniZinc-compatible solvers are best suited for floating decision variables and non-linear constraints?
Some of the coin-or open-source solvers like "couenne" can be used via MiniZn. You can follow the instruction of installation in this link.
Info about Couenne:
Couenne (Convex Over and Under ...
- 8,622
4
votes
Accepted
Can we use continuous variables instead of binary variables in this NLP problem?
Yes, binaries can be replaced by NLP using continuous variables. But it's not necessarily a good idea, and is usually is a bad idea. If it were a good idea, there probably wouldn't be MINLP solvers.
...
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4
votes
Can we use continuous variables instead of binary variables in this NLP problem?
You can relax integrality of $a_{i2}.$ Due to the "big M" constraints, I do not believe you can relax integrality of the other binary variables. It's a bit hard to be sure, since you did not ...
- 37.9k
4
votes
Which MiniZinc-compatible solvers are best suited for floating decision variables and non-linear constraints?
Of the constraint based solvers JaCoP (https://github.com/radsz/jacop ) and Gecode (https://www.gecode.org/) has support for float decision variables combined with nonlinear constraints. Choco (https:/...
- 914
3
votes
Accepted
Convex optimization on the unit hypercube with gradients and a bounded minimum
From the looks of it (simple feasible set, convex objective, gradient available), Frank-Wolfe indeed makes a lot of sense here.
I can point out that there exist many variants of the algorithm, and ...
- 4,068
3
votes
Accepted
Continuous water-filling optimization problem
Using Calculus of Variations as an inspiration we have the lagrangian
$$
\mathcal{L}(f,\lambda) = \int_0^{x_{max}}\left(-\ln\left(\alpha(x)+f(x)\right)+\lambda\left(f(x)-\frac{1}{x_{max}}\right)\right)...
- 146
3
votes
Continuous water-filling optimization problem
I can't tell if your path is right (because it depends on that you want to do), but it is sensible.
Your problem structure is quite similar to one occurring in the field of optimal control. I'm not ...
- 3,975
3
votes
Maximization of a differentiable and nonlinear function over a bounded space
The KKT conditions are necessary conditions for an optimum to your problem, so if you can find all feasible points satisfying them, the one with the best objective function will be your optimum. There ...
- 37.9k
2
votes
LPs having a 'stable' objective value wrt changes in the constraint right-hand sides
The property that some infinitesimal change in one of the constraints impacts the objective is called "a constraint being active" or "a constraint being in conflict with the objective&...
- 3,975
2
votes
Convex optimization on the unit hypercube with gradients and a bounded minimum
I hesitate to suggest it, since gradient methods tend to be faster than non-gradient methods, but the Nelder-Mead "simplex" algorithm is easy to code and might be worth a try.
- 37.9k
2
votes
Convex optimization on the unit hypercube with gradients and a bounded minimum
When you have only box constraints I don't think Frank Wofle is very efficient. Frank Wolfe can handle more complex constraints. You should try a quasi newton algorithm like l-bfgs-b or a truncated ...
- 121
2
votes
Armijo Line Search Parameters
You are correct that the optimal choice of parameters for the Armijo line search can vary depending on the problem and the optimization algorithm being used. In practice, there are several common ...
- 184
2
votes
Assignment Problem with continuous decision variable
Is there even a possibility that the mathematical optimal solution is
a continuous value
I would say it depends on the parameterization, i.e., the values of c and t and b in your problem. From your ...
- 136
1
vote
Requesting references about recursive functions where the variables are continuous
If the intent is to optimize $f_N(y)$ for some fixed $N,$ it might be a form of dynamic programming.
- 37.9k
1
vote
Represent the minimum between two terms as a continuous constraint
As far as i know you will have to
resort to a bi-level optimzation problem:
$\min_{A,B} x $ subject to ($\max_x$ subject to $x\leq A$ $x \leq B$)
solve a series of non linear problems where you ...
- 3,975
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