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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
863 views

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, $\|v\|_2=1$.
hichem hb's user avatar
  • 377
1 vote
1 answer
130 views

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 …
hichem hb's user avatar
  • 377