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Results tagged with convex-optimization
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user 4312
Optimization with convex constraints and convex objectives; notions related to convex optimization such as sub-gradients, normal cones, separating hyperplanes
2
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Famous theorems that are special cases of linear programming (or convex) duality
Bondareva–Shapley_theorem is quite famous in a game theory. In more modern terms, it unites the usual and dual description of the generalized permutohedron.
7
votes
Accepted
Maximizing trace subject to two equality constraints
If ${\rm rank} \, X>1$, there exists a two-dimensional space $\mathcal{L}$ such that the restriction of $X$ to $\mathcal{L}$ is positive definite. The space of Hermitian operators, which vanish on $\ …
- 109k
4
votes
Accepted
Is this function always bounded below?
Now I think that no, even if we remove the negative summands $-x_i+(1-x_i)\log(1-x_i)$. Note that our inequality becomes homogeneous, so we may forget that $x_i$ are less than 1. Choose $x_i=1+t_i$ so …
- 109k