12 votes
Accepted

What global MINLP solvers support trigonometric functions?

SCIP does not currently support any trigonometric functions as of this post from May 2018. COUENNE appears to handle $\sin$ and $\cos$ expressions. ANTIGONE appears to not support any trigonometric ...
Michael Feldmeier's user avatar
11 votes
Accepted

Simulation optimisation: Monte carlo simulation, regression, optimise within regression model?

After further reading it seems that "surrogate models" do exactly this (aka. "meta-models"), a recent discussion of methods is here: https://onlinelibrary.wiley.com/doi/full/10.1111/itor.12292 Also ...
Brendan Hill's user avatar
7 votes

What global MINLP solvers support trigonometric functions?

Here is an option for MATLAB users which is not mentioned in any other answers. YALMIP's BMIBNB iI a global branch and bound solver https://yalmip.github.io/solver/bmibnb/. It is used in combination ...
Mark L. Stone's user avatar
6 votes
Accepted

Forbid transformation of max(x,y) into MILP

In YALMIP you can use arbitrary black-box operators to circumvent modelling ...
Johan Löfberg's user avatar
6 votes
Accepted

Finding the global minimum of $f(\mathbf{x})=\|(1-x_1,x_1-x_2,x_2-x_3,\ldots,x_{n-1}-x_n,x_n-2)\|_2^2$

Cross-posting. The math looks good but why starting with $\nabla f(x) = 0$ instead of $\frac{1}{2}\nabla f(x) = 0$? You should have noticed that the factor $2$ was everywhere and could be simplified. ...
f10w's user avatar
  • 176
6 votes

Heuristic methods for optimising complex black box function over permutations/ranks?

An approach that is easy to implement and always worth a shot is a simple neighborhood search, where you start with some candidate solution and iteratively move to a neighbor solution. For your ...
Rolf van Lieshout's user avatar
6 votes

Simulation optimisation: Monte carlo simulation, regression, optimise within regression model?

You might want to google "response surface methodology" and "simulation" together. There is a ton of literature on this, a mixture of how do to response surface modeling (and how to use it to optimize ...
prubin's user avatar
  • 39.1k
6 votes

What global MINLP solvers support trigonometric functions?

From the presentation given by Vigerske, S. (2015), it is noted that the solvers Couenne by P. Belotti and LindoAPI by Y. Lin and L. Schrage can handle trigonometric expressions. Both are ...
ə̷̶̸͇̘̜́̍͗̂̄︣͟'s user avatar
6 votes
Accepted

Scipy.optimize can't get correct answer when objective is Piecewise Linear Function and Equality Constraint

You are trying to minimize a concave function, and minimize finds only a local minimum. To find a global minimum, use one of the methods under "Global ...
RobPratt's user avatar
  • 32k
5 votes
Accepted

Black-box optimization of a single parameter function with high cost evaluation

Given that your function is apparently unimodal (single local minimum, which is global), you might try golden section search. The first four function evaluations result in about a 40% reduction in the ...
prubin's user avatar
  • 39.1k
5 votes

What global MINLP solvers support trigonometric functions?

Octeract Engine (the solver I develop), is a deterministic global MINLP solver that supports all trigonometric functions (including hyperbolic functions).
Nikos Kazazakis's user avatar
5 votes

On the global optimization solver Octeract

Thanks for your interest. We discontinued the free version in 2022 due to various reasons, and the solver has been a paid product for all audiences ever since. Our Neural service is free, but it's ...
Nikos Kazazakis's user avatar
5 votes
Accepted

Global optimizers handling minimization of expressions like $\log{v}+\frac{1}{v}$

The logarithm is not a convex function, so even though the expression as a whole is convex on some subinterval $v \in [c,d]$, the expression is not in disciplined convex form which might be why yalmip ...
Henrik Alsing Friberg's user avatar
4 votes
Accepted

Global Optimization when the exponential function is involved

This is a non-convex global optimisation problem. The state-of-the-art way to solve this is to use a factorable relaxation. A key insight here is that $e^{-\alpha X}$ is convex (since your $\alpha$ is ...
Nikos Kazazakis's user avatar
4 votes

Global Optimization when the exponential function is involved

Assuming the continuous relaxation is convex you can most likely use conic optimization with the exponential cone. The Mosek modelling cookbook has the details. Unsurprisingly Mosek can solve the ...
ErlingMOSEK's user avatar
  • 3,166
4 votes

General Optimization and Unsolvability

General global optimisation problems are solvable in finite time and in a finite number of steps, under the following assumptions: All mathematical expressions are available (i.e. not black-box ...
Nikos Kazazakis's user avatar
4 votes

Prove NP Hardness for non-convex multi-objective optimization

The notion of NP-hardness relates to whether one class of problems can be solved by a solver for another class of problems where the translation overhead is negligible. The problem you presented is ...
worldsmithhelper's user avatar
4 votes

Forbid transformation of max(x,y) into MILP

The default Octeract Engine behaviour is to handle this automatically without reformulating to an MILP.
Nikos Kazazakis's user avatar
4 votes
Accepted

How to prove that optimizing each component of a system separately gives suboptimal result?

Method #1 is called local optimization, while Method #2 is called global optimization. In practice, all modelling is local. That is, we have to draw a boundary around the parts of the whole system ...
Solver Max's user avatar
3 votes

Prove NP Hardness for non-convex multi-objective optimization

NP-hardness is an asymptotic result of increasing problem dimensions. It is not a property of one fixed problem instance. So to ask whether your problem class is NP-hard, you would have to explain how ...
prubin's user avatar
  • 39.1k
3 votes

Transportation problem with consolidation within path

If your demands are per source-destination pairs, then you are very likely dealing with a variation of the multi-commodity flow problem, where each source-destination pair is a commodity. The ...
Kuifje's user avatar
  • 13.3k
3 votes

How to prove that optimizing each component of a system separately gives suboptimal result?

To add the answer by @solver max (I think it is a very good answer), Please be aware that, neither method-$1$ nor method-$2$ has a preference over another. Specifically, for the black-box optimization,...
A.Omidi's user avatar
  • 8,882
3 votes

Heuristic methods for optimising complex black box function over permutations/ranks?

A "random key" genetic algorithm (henceforth RKGA) might get you a pretty good solution within your function call limit (particularly if you cache function values, so that repeated evaluations of the ...
prubin's user avatar
  • 39.1k
3 votes

Global optimality condition of non-convex quadratic programs

In addition to the references already given in the comments, this paper (DOI link) demonstrates that exact solutions to some non-convex quadratic programs are given by semi-definite programming, and ...
Ryan Cory-Wright's user avatar
3 votes

Piecewise linear and global optimization

I might be missing something here (and by "might be" I mean "probably am"), but at least for the case of $x_i \in [0,1]$ you might be able to get solutions via "brute force&...
prubin's user avatar
  • 39.1k
3 votes
Accepted

Piecewise linear and global optimization

As far as I can see there is no exact convex reformulation for this, unless someone else can think of a nice trick. Constraint 1 can actually be convexified for certain ranges of $q_i$ as these ...
Nikos Kazazakis's user avatar
2 votes

Global optimality condition of non-convex quadratic programs

With the exception of special cases, this problem is NP-hard. One interesting case is that minimizing a convex or concave function over a simplex can be solved in polynomial time. In other special ...
Nikos Kazazakis's user avatar
2 votes

Global Optimization when the exponential function is involved

You may find a partial answer to your question in the following article (forthcoming in OR) by JP Vielma and J Huchette https://arxiv.org/abs/1708.00050 In that paper, the authors consider the problem ...
Claudio Contardo's user avatar
2 votes

Black-box optimization of a single parameter function with high cost evaluation

I would advise Bayesian Optimization. The benefits imho are that they don’t require a gradient, work for a wide variety of optimization problems and are made for when we are dealing with functions ...
Steven01123581321's user avatar
2 votes

General Optimization and Unsolvability

I had a look at your paper. Here are two errors that I think are worth reflecting about: You are assuming computations in finite precision, and consider solving a continous optimization problem. We ...
Ggouvine's user avatar
  • 1,877

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