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Results tagged with convex-optimization
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user 36356
Optimization with convex constraints and convex objectives; notions related to convex optimization such as sub-gradients, normal cones, separating hyperplanes
8
votes
1
answer
1k
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Uniqueness of a Solution for a Convex Optimization Problem
I have the following convex optimization problem:
$$\begin{array}{ll} \text{maximize}_{{f,g}} & \displaystyle\int_{\Omega} g^u{f}^{1-u}\mathrm{d}\mu\\ \text{subject to} & \displaystyle\int_{\Omega} f …
- 359
4
votes
0
answers
227
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Minimization over a convex function of equal vs unequal success probabilities of Bernoulli r...
Let $U_1,U_2,\ldots,U_n$ be $n\geq 2$ mutually independent Bernoulli random variables. There are two cases of interest:
$1.$ The random variables $U_1,U_2,\ldots,U_n$ are identically distributed;
$U_ …
- 359
3
votes
1
answer
950
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On compactness in Sion's minimax theorem
Sions minimax theorem (wiki, paper) can be stated as follows:
Let $X$ be a compact convex subset of a linear topological space and $Y$ a convex
subset of a linear topological space. Let $f$ be a …
- 359
2
votes
1
answer
113
views
Does maximizing $D_u$ imply stochastic ordering?
Let $\mathscr P _0$ and $\mathscr P _1$ be two non-overlapping sets of probability distributions defined on $(\Omega,\mathcal{A})$. Consider the distance defined as $$D_u(P_0,P_1)=\int_\Omega \left(\f …
- 359