# 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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### 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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 (-...
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 ...
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 $f(\mathbf{x})=\|(1-x_1,x_1-x_2,x_2-x_3,\ldots,x_{n-1}-x_n,x_n-2)\|_2^2$ ...
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 ...
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 (...