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Optimization with convex constraints and convex objectives; notions related to convex optimization such as sub-gradients, normal cones, separating hyperplanes
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Minimization problem involving the inverse of an affine matrix function
I want to minimize $v^T (A+I+UQU^*)^{-1} v$, subject to $Q$ and $A$ being positive semi-definite and ${\rm trace}(Q)<1$. Here, $v$ is a given vector with unit norm, that is, $\|v\|_2=1$.
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find a PSD matrix that that verify matrices sum of equality
$A $, $ C$ $(n,n)$ are symmetric PSD matrices,
$B$ is PD symmetric matrix, and $H_i$ $\; $ $(i=[1,m])$ represent $ m $ complex matrices. $H_i$ are all one rank matrix
Our objectif is to find P …