# Questions tagged [global-optimization]

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### Transformation of an unconstrained binary quadratic optimization problem into a constrained binary linear programming problem

I know that a constrained linear optimization problem can be transformed into an unconstrained binary quadratic optimization problem (UBQP). Does anyone know if the inverse result is solved in the ...
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### Pros and cons of using integer programming alone or combined integer and global optimization?

First, I am not sure if this is the right question to ask in this forum. But I have been looking for answers for a long time and I have been also asking my university's "engineering" professors but I ...
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### When does $\min_x \max_yf(x,y) = \min_y \max_x f(x,y)$ hold for a real function $f(x,y)$?

Let $f(x,y)$ be a real function of the variables $x,y$ (which can be real vectors). Under what conditions do we have the following equality: $$\min_x \max_yf(x,y) = \min_y \max_x f(x,y)$$ For ...
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### Joint optimization of the order 1 moment of a function and its Fourier transform

For the purpose of a quantum optics experiment, I come to the following problem : Let $X,P \in \mathbf{R}^2$ \begin{equation} J(\psi) = | \int_{-X}^{X} x |\psi^2(x) | dx + \int_{-P}^{P} p |Tf(\...
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### Is there a multiplier rule for this minimization problem?

Let $(E,\mathcal E)$ be a measurable space, $W\subseteq\left\{w:E\to\mathbb R\mid w\text{ is }\mathcal E\text{-measurable}\right\}$ be a Banach space, $k\in\mathbb N$ and $f:W^k\to[0,\infty)$. I'm ...
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### Are those two Sum-Of-Squares approach for unconstrained polynomial optimization related?

I found 2 approaches to solve an unconstrained polynomial optimization problem using the Lasserre / SOS hierarchy: $$\inf_{x\in\mathbb{R}^n}\quad p(x),$$ where $p$ is a polynomial of even degree ...
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Let $I$ be a finite set, and $A_{ij},B_{ij},x_i,y_j\ge0$. I want to find the choice of $x_i,y_j$ maximizing $$\sum_{i\in I}\sum_{j\in J}A_{ij}\min\left(x_i,B_{ij}y_j\right)\tag1$$ subject to \sum_{i\...