I want to solve the following optimization problem <mtext>maximize&#xA0;</mtext> f (

Carina Valenzuela 2022-05-08 Answered
I want to solve the following optimization problem
maximize  f ( X ) = log d e t ( X + Y ) a T ( X + Y ) 1 a subject to  X W ,
where the design variable X is symmetric positive semidefinite, W , Y are fixed symmetric positive semidefinite matrices, and a is a given vector. The inequality X W means that X W is symmetric positive semidefinite.

I was wondering if there's hope to find an analytical solution to either the constrained or unconstrained problem. And if there is none, could I use convex optimization techniques to solve this numerically?
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Answers (1)

Raiden Williamson
Answered 2022-05-09 Author has 14 answers
Make the substitution Z = ( X + Y ) 1 X = Z 1 Y, then the problem becomes convex:
maximize  log d e t ( Z ) a T Z a subject to  0 Z ( Y + W ) 1
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