Quad_form for convex problem (Moderator note: quad_form is convex, but this problem is not)

Nonconvex
1

if i have the following optimization problem the variable is only Wtc:
minimize( norm(y_r-H*Wtc,'fro')+norm(f - pinv(Pq)*vec(Wr1*G*Wtc'*Wtc)),'fro')) to over come the multiplication of Wtc'*Wtc i used the following
minimize( norm(y_r-H*Wtc,'fro')+norm(f - pinv(Pq)*vec(Wr1*G*quad_form(Wtc, eye(Nt))),'fro'))
but the cvx give the following error Error using .*
Disciplined convex programming error:
Cannot perform the operation: {complex affine} .* {convex}

Error in * (line 36)
z = feval( oper, x, y );

Error in solv_z_problem_SU (line 61)
minimize( norm(y_r-HWtc,‘fro’)+norm(f - pinv(Pq)vec(Wr1Gquad_form(Wtc, eye(Nt))),‘fro’))

2

quad_form` is accepted by CVX, and produces a convex result. BUt multiplying that by (complex) affine is not allowed.

Have you proven this is a convex optimization problem? it doesn’t appear to be.

3

the problem in general is
minimize( norm(y_r-H*Wtc,'fro')+norm(f - pinv(Pq)*vec(Wr1*G*Wt)),'fro')) where Wt = Wtc'*Wtc as far as i know both are norm and convex the first norm is convex with respect to Wtc and the second norm is convex with respect to Wt but the problem appears when Wt=Wtc'*Wtc by the wat Wtc is vector (N,1) and Wt is matrix (N,N). Thus i want to include Wt=Wtc'*Wtc for problem and maintain the convexity.

4

Wanting to maintain convexity is different than maintaining convexity. Please re-read the link.

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