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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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}
\...
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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?
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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 ...
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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 ...
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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} (\...
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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 ...
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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 ...
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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 (...
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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 ...
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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 ...
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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 (-...
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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 ...
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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
$f(\mathbf{x})=\|(1-x_1,x_1-x_2,x_2-x_3,\ldots,x_{n-1}-x_n,x_n-2)\|_2^2$
...
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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 ...
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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 ...
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MINLP Solution same as Global Optimum?
Is the solution to an MINLP problem the global optimum to this problem?
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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 ...
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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 ...
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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 ...
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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 ...
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