Questions tagged [global-optimization]

For questions on optimization problems that seek solutions that are globally optimal (in contrast to locally optimal solutions).

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13
votes
4answers
468 views

What global MINLP solvers support trigonometric functions?

What (deterministic) global optimization packages support trigonometric functions such as $\sin, \cos, \tan$ in the constraints or objective function? What limitations do they have? I am not asking ...
13
votes
2answers
497 views

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

Can you help me identify if this technique has a standard name to help me explore the literature? Suppose I have a black-box stochastic simulation parameterised by $X=[x_1,...,x_p]$ with some single ...
10
votes
2answers
106 views

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

Suppose I have a set $S=\{1,2,\dots,500\}$ and some function $f(\sigma)$ from the permutations $\operatorname{Perm}(S) \rightarrow \mathbb{R}$ to be minimized. The function is complex (simulation ...
10
votes
2answers
150 views

Global optimality condition of non-convex quadratic programs

We know that a convex quadratic maximization (not minimization!) on a polyhedron has its global optimal value on a vertex. Also, I have read in some papers that checking whether a vertex is globally ...
6
votes
2answers
240 views

Forbid transformation of max(x,y) into MILP

The function $\max(x,y)$ can be linearized by making use of additional binary variables. I suppose global optimisers are implemented to perform this transformation automatically. Is there a global ...
5
votes
3answers
203 views

Global Optimization when the exponential function is involved

I wonder if there are methods to determine the global optimum of MINLP problems, when the nonlinear functions involved are only of the form $Z = Y e^{- \alpha X}$, where $Y \ge 0$ and $X \ge 0$. Are ...
5
votes
2answers
119 views

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

I need to solve a series of single parameter black-box minimization problem. The underlying cost functions are quite simple. They always have the same shape: a global minimum inside a fixed interval (-...
5
votes
2answers
189 views

Piecewise linear and global optimization

I am new to OR, and apologies if my mathematical notation is not clear. I have tried my best to keep it concise and given an explanation with numerical data. I would like to understand: Can this ...
4
votes
1answer
105 views

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

I am self-learning optimization algorithms. A certain assignment problem is as follows: Show that the $n$-dimensional function $f(\mathbf{x})=\|(1-x_1,x_1-x_2,x_2-x_3,\ldots,x_{n-1}-x_n,x_n-2)\|_2^2$ ...
3
votes
2answers
193 views

General Optimization and Unsolvability

Can someone tell if it is known that if finding global optima is unsolvable (in Turing sense). I have posted an arXiv paper https://arxiv.org/pdf/2103.13821.pdf showing this. But I'm not sure if it is ...
2
votes
2answers
88 views

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

The black-box system shown below has 3 components. They run sequentially to generate a final output from the input. Each component has its own parameters to optimize for better intermediate results (...
2
votes
2answers
72 views

MINLP Solution same as Global Optimum?

Is the solution to an MINLP problem the global optimum to this problem?
1
vote
3answers
191 views

Prove NP Hardness for non-convex multi-objective optimization

The multi-objective optimization problem in my case is non-linear as it consists of three objective function of which two are nonlinear function and the third is a linear function. Lets say objective ...