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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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Optimization under cardinality constraint

When we consider the following optimization problem: \begin{equation}\label{P}\tag{P} \begin{array}{ll} \displaystyle\min_{x \in \mathbb{R}^n} & f(x) \\ \text{s.t.} & Ax = b,~ x \geq 0, \\ &...
Optimization Online's user avatar
0 votes
0 answers
39 views

Scaling of objective function changes convergence

I am trying to solve a nonlinear program using the global optimization solver BARON. The problem has roughly 2e4 variables and also several thousand equality and inequality constraints. Being aware of ...
jamieil's user avatar
2 votes
0 answers
161 views

Global optimizers handling minimization of an expression arising from the likelihood of a multivariate normal

I am interested in converting the following optimisation problem into a form that an exponential cone and/or SDP solver such as MOSEK can handle. This is a multivariate version of the question I ...
cfp's user avatar
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3 votes
1 answer
885 views

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

I'm encountering a puzzling issue with SciPy's minimize function in a constrained optimization problem. My objective is to optimize a piecewise linear function with ...
Yiyuan Chen's user avatar
5 votes
2 answers
175 views

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

Consider the simple problem of maximum likelihood estimation of the variance of a mean zero normal distribution. The expression to be minimised is: $$N \log{v}+\frac{1}{v}\sum_{n=1}^N{b_n^2},$$ where $...
cfp's user avatar
  • 259
2 votes
0 answers
38 views

Addressing Variable Multiplication in Constrained Infinity-Norm Maximization with Hypercube & Polyhedron Constraints

I am reaching out to this knowledgeable community for assistance with a complex optimization problem that I have been investigating. Here is the formulation of the problem I'm addressing: $$\tag{1} \...
Diego Fonseca's user avatar
0 votes
1 answer
129 views

Linear Programming faster solver: CPLEX or Gurobi?

Which one is the best solver for solving large-sized problems in Linear Programming, CPLEX or Gurobi? Which one is faster?
Optimization Online's user avatar
1 vote
1 answer
61 views

Is there any literature on constrained nonlinear optimization where constraint returns have to be queried from an oracle?

I am looking at literature considering constrained optimization problems of the form: $\min_{x\in X\subseteq R^n} f(x), \text{ subject to } g_{oracle}(x) \leq 0$ The optimization algorithm doesn't ...
Shourya Bose's user avatar
4 votes
1 answer
293 views

On the global optimization solver Octeract

A while back, I read on this forum that Octeract is free for academic use and that for commercial use it is also free but users are restricted to 1 core. I cannot find anything on the website to ...
Enthusiast's user avatar
2 votes
2 answers
129 views

Optimize least squares penalized by curvature of log pdf

I have probability values $p \in \mathbb{R}^n$. Given $A \in \mathbb{R}^{m\times n}$, $b \in \mathbb{R}^m$, I want to minimize the following objective function. $||Ap - b||_2^2 + \sum_{i=1}^{n-2} (\...
JEK's user avatar
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2 votes
1 answer
186 views

Solving a Global Optimization problem using Differential Evolutionary Algorithm using R

I need to determine the global optimum results of this objective function. I define the problem by minimizing the squared difference as represented in function $f(q_1,q_2,\alpha_1,\alpha_2)$ The ...
Mrinmoy Chakraborty's user avatar
3 votes
2 answers
130 views

Transportation problem with consolidation within path

There's a supply network design problem that I'm trying to solve, which is as follows: A certain amount of goods need to be transported from point A to B, and can have stoppages in between with a ...
J. Alan's user avatar
  • 31
2 votes
2 answers
192 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 (...
idwwwoqq808's user avatar
3 votes
2 answers
231 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 ...
Lakshmanan K's user avatar
1 vote
3 answers
325 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 ...
vp_050's user avatar
  • 179
5 votes
2 answers
141 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 (-...
Kh4zit's user avatar
  • 175
6 votes
2 answers
333 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 ...
Clement's user avatar
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5 votes
1 answer
127 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 $f(\mathbf{x})=\|(1-x_1,x_1-x_2,x_2-x_3,\ldots,x_{n-1}-x_n,x_n-2)\|_2^2$ ...
Quasar's user avatar
  • 203
5 votes
2 answers
339 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 ...
Marry's user avatar
  • 81
5 votes
3 answers
597 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 ...
Clement's user avatar
  • 2,252
2 votes
2 answers
133 views

MINLP Solution same as Global Optimum?

Is the solution to an MINLP problem the global optimum to this problem?
Clement's user avatar
  • 2,252
10 votes
2 answers
184 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 ...
Brendan Hill's user avatar
13 votes
2 answers
559 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 ...
Brendan Hill's user avatar
10 votes
2 answers
241 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 ...
independentvariable's user avatar
13 votes
4 answers
840 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 ...
Michael Feldmeier's user avatar