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Results tagged with convex-optimization
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user 51546
Optimization with convex constraints and convex objectives; notions related to convex optimization such as sub-gradients, normal cones, separating hyperplanes
7
votes
1
answer
215
views
How to prove the existence of the polytope in $\mathbb{R}^d$ with a given number of faces, m...
This is the isoperimetric type question. We know that in $\mathbb{R}^d$, balls are the sets that minimize the isoperimetric ratio $\frac{S^{d}}{V^{d-1}}$, where $S$ is the surface area and $V$ is the …
- 1,350
5
votes
1
answer
341
views
Lower bound for total mean curvature among mean convex set in $3D$ with fixed volume
I learned that the sphere has the smallest total mean curvature among all convex solids with a given surface area. This actually implies the sphere also has the smallest total mean curvature among all …
- 1,350
3
votes
1
answer
446
views
How to find extreme points of a set related to Minkowski's Theorem?
Let $S^{n-1}$ be the unit sphere in $\mathbb{R}^n$. For $m>n$, we can define $\Lambda$ to be the set
$$\{(\lambda_1, ..., \lambda_m):\sum_{i=1}^m \lambda_i=1, \lambda_i\ge0, and \mbox{ there exist}\, …
- 1,350