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# Questions tagged [global-optimization]

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### Can the partial concavity of the following decomposable objective function be used for optimization?

The problem I am trying to solve is the following: $$\begin{array}{ll} \min & f(x)+g(y) \\ \mathrm{s.t.} & y\ge x\ge 0,\\ \ & p\le ax+by\le q, \end{array}$$ where $a,b,p,q$ are ...
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### Stochastic process for minimize a mean

I have the next problem: consider an inventory process $\{X_{k}\}$ such that $X_{k+1}=X_k+A_k-\xi$, $X_0=25$, where $A_k$ is the number of items of items produced at the $k$th-month and $\xi$ is the ...
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### On a maximum of a determinant with dependent variables

Let $x_1,\ldots,x_n\in [-1,1]^n$ and define the function $$f(x_1,\ldots,x_n):= \prod_{i=1}^n\prod_{j=i}^n\left(1-\prod_{k=i}^j x_k\right).$$ This is a positive function, and actually coincides with ...
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Let $M$ be a Riemannian manifold, and $G$ be a group of isometries on $M$. If we have a $G$-invariant functional $F: M \rightarrow \mathbb{R}$, i.e. $F(g \cdot x) = F(x)$ for all $x \in M$ and $g \in ... 1answer 114 views ### Finding$P$points among$N$to approximate a probability density function? Let$f$be a probability density function (positive such that$\int_{\mathbb{R}} f(x) \mathrm{d} x = 1$) and$X_0 = \{x_n\}_{1\leq n \leq N}$be$N$given real points. We also fix$1 \leq P \leq N$... 2answers 128 views ### Looking for a very particular kind of non-convex functions I want some examples (hopefully parametric families!) of non-convex functions which satisfy the following properties simultaneously, It should be at least twice differentiable. It should have a ... 0answers 45 views ### Minimum Preserving Transformations [closed] If$f:X\rightarrow Y$,$g:Y\rightarrow Y$are functions and$g\$ is monotone increasing function then $$\operatorname{argmin}_{x \in X} f(x) = \operatorname{argmin}_{x \in X} g\circ f(x) .$$ X and Y ...

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