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Results tagged with convex-optimization
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user 145424
Optimization with convex constraints and convex objectives; notions related to convex optimization such as sub-gradients, normal cones, separating hyperplanes
9
votes
1
answer
319
views
Closedness of linear image of positive L1 functions
Let $\mathcal X$ be the Banach space of $L^1$ functions on some probability space, $\mathcal Y$ be some other Banach space, $T:\mathcal X\to \mathcal Y$ be some surjective continuous linear map, $\mat …
- 537
4
votes
0
answers
135
views
A convex function is "usually" subdifferentiable
Let $X$ be a locally convex topological vector space, and let $f:X\to\mathbb R\cup\{\infty\}$ be a proper, convex, lower semicontinuous function, whose effective domain $D:=f^{-1}(\mathbb R)$ is compa …
- 537
4
votes
1
answer
181
views
Subgradient in a predual under weak* continuity
Let $X$ be a Banach space. Suppose $f:X^*\to\mathbb R\cup\{\infty\}$ is convex, has weak*-compact effective domain, and is weak*-continuous on its effective domain. In particular, $f$ is weak*-lower …
- 537
2
votes
1
answer
246
views
When is a function a convex conjugate?
Let $X$ be a Banach space; $X^*$ be its dual; and $g:X^*\to\mathbb R\cup\{\infty\}$ be a proper, convex, weak${}^*$-lower semicontinuous function with weak${}^*$-compact effective domain.
Question: Is …
- 537