Solving an SDP optimization problem

Nonconvex
1

I want to solve a semi-definite problem with CVX
I have some pairs of similar points in a set called S
and some pairs of dissimilar points in a set called D
And I want to find a symmetric positive semi definite matrix by solving problem in below:

min_ A ∑_((x_i,x_j∈S)) ‖x_i-x_j ‖_A^2

s.t ∑_((x_i,x_j∈D)) ‖x_i-x_j ‖_A >= 1
A>=0

where ‖x_i-x_j ‖_A = √((x-y)^T A (x-y))

but I don’t know how to write it in a format that can be solved by CVX

2

Your inequality constraints on D are nonconvex. If you squared each term in the summation then they would be linear in A. But what have you tried so far? This forum isn’t here to write models for you; it’s to help you once you get started with the code, the manual, and the examples.

3

FAQ: Why doesn’t CVX accept my problem? [READ THIS FIRST]