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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
1 answer
1k views

Maximization of log-sum-exp function

I am reading about robust optimization and there is a claim: $$ \max_{\mu^-\leq\mu\leq \mu^+} \ln \left( \exp\left\{w+\ln\left(\frac{1+\mu}{2}\right)\right\} +\exp\left\{-w+\ln\left(\frac{1-\mu}{2}\ …
Eggplant's user avatar
0 votes
0 answers
104 views

How to find a set given its support function

Let $\mathcal{U}$ be a convex and compact set. Its support function is defined as $\delta^*(v|\mathcal{U})=\sup_{u\in \mathcal{U}} v^T u$. Assume that we are given the support function $\delta^*(v|\ma …
Eggplant's user avatar
3 votes
1 answer
152 views

Duality problem of an infinite dimensional optimization problem

I am reading the paper "OPTIMAL INEQUALITIES IN PROBABILITY THEORY: A CONVEX OPTIMIZATION APPROACH" by BERTSIMAS and POPESCU. In the paper, the authors derived a duality problem for an infinite-dimens …
Eggplant's user avatar