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Results tagged with convex-optimization
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user 12518
Optimization with convex constraints and convex objectives; notions related to convex optimization such as sub-gradients, normal cones, separating hyperplanes
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answers
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Minimizing total variation under constraint
For $p\in[0,1]$, we write $\mathrm{Ber}(p)$
to denote the Bernoulli measure on $\{0,1\}$;
that is, $\mathrm{Ber}(p)(0)=1-p$,
$\mathrm{Ber}(p)(1)=p$.
For $n\in\mathbb{N}$ and $p=(p_1,\ldots,p_n)\in[0,1 …
- 6,367
5
votes
0
answers
252
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Generalized convexity
Let $X$ be a vector space. The positive-homogeneous function $\|\cdot\|$ is said to be a quasinorm
if $\|x+y\|\le K(\|x\|+\|y\|)$, for some $K\ge1$; it is a norm if $K=1$.
Question: 1. (terminology) i …
- 6,541
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answers
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Variant of Sion's minimax theorem
Sion's minimax theorem assumes that $f:X\times Y\to\mathbb{R}$ is being minimized w.r.t. $x$ and maximized w.r.t. $y$, where at least one of $X,Y$ is compact (additional (quasi)convexity and semi-cont …
- 6,541