# Questions tagged [extreme-points]

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Consider the maximization problem $$\text{maximize} \quad Q(x)= \sum_{i<j} \Big(\sum_{k} a_{ik}a_{jk}\Big) x_i x_j \quad \text{subject to} \quad \sum_{i}x_i^2=1,$$ and let $M$ be maximum value ...
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### Extreme points of an intersection of convex set with countably many linear spaces

Let $V$ be some `nice' vector space and let $T: V\to \mathbb{R}$ be a linear functional over $V$. Define \begin{align} M= K \cap \bigcup_{i \in \mathbb{N} } \{ v \in V: T(v)=c_i \} \end{align} ...
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### A Banach space where the closed unit ball is the convex hull of its extreme points

Let $X$ be a Banach space where the closed unit ball equals the convex hull of its extreme points. Is it true that this implies $X$ is reflexive?
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### Extreme points of set of measures with given barycenter

Let $X$ be a convex compact metrizable subspace of a locally convex Hausdorff topological vector space, $x_0\in X$, and $P$ be the space of all Borel probability measures on $X$ with barycenter $x_0$. ...
Let $L^2$ be the set of all square-integrable functions $f:[0,1] \to [0,1]$ and $S \subset L^2$ be a closed and convex subset of $L^2$ containing the function that is constant and equal to zero. Are ...