# Questions tagged [global-optimization]

Global optimization is a branch of applied mathematics and numerical analysis that attempts to find the global minima or maxima of a function or a set of functions on a given set.

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### get Jacobian for fminsearch

I am using MATLAB function lsqnonlin to get the optimal parameters for a system of ODE. lsqnonlin by default gives an option to get the Jacobian. Now, when I am trying to get the same parameters using ...
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### Question on continuity and optimization

Let $f:\mathbb{R}^2\to\mathbb{R}$ be a continuous function on $\mathbb{R}^2$. Is it true that, if $$\lim_{||(x,y)||\to{\infty}}{f(x,y)}=-{\infty}$$ then $f$ has a global maximum on $\mathbb{R}^2$...
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### Proof global minimum in two dimensions WITHOUT hessian but based on limit behavior

Consider a function $\Phi \colon D \to \mathbb{R}$, $D = \{(x,y) \in (0,\infty)^2 \mid x < y\}$, $\Phi$ differentiable on $D$. It is known, that $(x^\ast,y^\ast)$ is the only critical point in $D$ ...
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### Coercive/(weakly) semicontinuous function: extreme values

Consider functionals of the form $$\phi : X \rightarrow \mathbb{R} \cup\{+\infty\},$$ where $X$ is an arbitrary, normed vector space. In particular, $X$ may be of infinite dimension. I would be fine ...
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### Why is it difficult to find the Global Optimum?

When studying Calculus I learnt that it it possible to take the derivative of a function to find its minimum and maximum points. I then wondered what happens if there are more than one minimum and ...
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### Is there any way to solve df(t)/dt = 0 for t and f(tsolved) value if we know F(s), the Laplace transform of f?

I am trying to know max(f(t)) value but I have only F(s) equation of it and I thought that by solving df(t)/dt == 0 by Laplace using F(s) which is s*F(s) == 0, I can easily solve what is t for max(f(t)...
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### Rigorous global optimization

The work by Thomas Hales (see enter link description here) before the formal proof solves a number of global optimization problems that need to be solved exactly. The strategy relies on following ...
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### Any comprehensive books on global smooth optimization?

Can you share any information about books that review most of the existing numerical methods for global minimization of a multivariable objective function? The objective and constraints are assumed ...
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### Global optimization of non-smooth function

I have a number of functions (see for example two of them down below), and I need to find their global optimum for each of them. They are non-smooth, but they are always funnel-shaped, exhibiting a ...
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### Can basin-hopping be applied for global constrained optimization?

Can we implement Basin-Hopping approach for constrained optimization problems ? The literature suggests it for unconstrained global optimization, but I have a few constraints. Can it be adapted for ...