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Optimization with convex constraints and convex objectives; notions related to convex optimization such as sub-gradients, normal cones, separating hyperplanes

1 vote
0 answers
171 views

continuity of linear programming

I have the following conjecture: Given a closed convex set $S \subseteq \mathbb{R}^n$ and one of its exposed face $F=\{x \in S \mid \pi x = \pi_0\}$, where $\pi x =\pi_0$ is the supporting hyperplane …
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1 answer
153 views

Generalization of Dickson's Lemma

Given $\{v^i\}_{i \in \mathbb{N}} \subseteq \mathbb{N}^n$, and $\cup_{k=1, \ldots, m} C_j = \mathbb{N}^n$ for some $m$, where each $C_k$ is a cone generated by rational vectors. My question is: does t …