How to DC method representation for the rank-one constraint in CVX

[ESLAM-MOHAMMED23 (ESLAM SAEED)]

W0 is a PSD matrix and Tr(W0) > 0, the rank-one constraint
rank(W0) = 1

and how linearize the concave terms

by using the majorization-minimization technique

(1) how can i write this equation in CVX and solved it

[Mark_L_Stone]

As I posted on your previous question, how to do DC representations and how to use the majorization-minimization technique are out of scope of this forum.

But if someone wants to post how, they are free to do so.

You may (or may not) find this post from @stephen_boyd helpful as to a heuristic (non-guaranteed) way to deal with non-convex usage of two-norm.

How to handle nonlinear equality constraints?

mcg’s answer is correct; the problem is not convex, and cannot be expressed in DCP format. more specifically, a constraint like \|Aw\|_2 \leq P (with A a constant matrix and w a variable) is OK (convex, and DCP), but the converse constraint, \|Aw\|_2 \geq P, is not convex, and (therefore) not DCP. i’d like to add that there are heuristic methods for “handling” such problems, using the so-called convex-concave procedure (see EE364b, lecture on sequential convex programming). this is a heuris…