# 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: \label{P}\tag{P} \begin{array}{ll} \displaystyle\min_{x \in \mathbb{R}^n} & f(x) \\ \text{s.t.} & Ax = b,~ x \geq 0, \\ &...
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 ...
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 ...
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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 ...
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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 ...
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 ...
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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 (...
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 ...
1 vote
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 ...
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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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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 ...
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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 $f(\mathbf{x})=\|(1-x_1,x_1-x_2,x_2-x_3,\ldots,x_{n-1}-x_n,x_n-2)\|_2^2$ ...
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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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133 views

### MINLP Solution same as Global Optimum?

Is the solution to an MINLP problem the global optimum to this problem?
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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 ...
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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 ...
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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 ...
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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 ...
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