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# Questions tagged [global-optimization]

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### Matrix optimization to find ideal embedding

Basically, I am trying to find the embeddings so I can approximate $K \approx M(\vec{\phi})$. The embeddings are for each one of my samples $\vec{\phi}(x_i) \in \mathbb{R}^D$ so I thought it should ...
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### Minimize total area bounded by $N$ lines in general position

Suppose we have $N$ lines in general position (any two lines, but no three lines, meet at a point) ($N\geq 3$). Let the smallest bounded region have area $1$. Determine the minimum (or possibly ...
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### Known configurations maximizing the volume of the convex hull of n points on the unit sphere

For $n\geq 4$, let $V_n$ be the maximum volume of the convex hull of $n$ points on the unit sphere (in $\mathbb{R}^3$, although information on higher dimensions is welcome as well). I'm sure the ...
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### Optimal Kelly criterion for process with N discrete outcomes

I am trying to come up with a generalisation of the Kelly formula for optimal fractional betting but and have hit a roadblock. The Kelly criterion is usually explained via a game that ends in 1 of 2 ...
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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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### 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 ...