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

4 votes
1 answer
123 views

Maximizing trace subject to two equality constraints

I am looking at the following optimization problem $$\begin{align} \underset{{\bf X}}{\text{maximize}} \qquad&\mathrm{tr}({\bf AX})\\ \text{subject to} \qquad& \mathrm{tr}({\bf X}) = 1,\\ &\mathrm{tr …
0 votes
0 answers
60 views

Minimizing the Spectral Norm of the Hadamard Product of a Quadratic Form Using CVX

I am trying to use CVX to minimize the spectral norm of the Hadamard product of two matrices, one of which is in quadratic form. Specifically, I am trying to minimize $\|{\bf A} \odot {\bf XX}^H\|_2$, …