Cvx maximization problem

Hi, I have an optimization problem whose optimum solution is known. However I could not re-produce it myself.

The problem

I know K (16x16) and s_i =SMP(:,ii) where SMP is (4x16) . Both of these variables are non-complex. W is the optimum precoding matrix. I wrote this problem as below


variable t nonnegative
variable W(4,4) nonnegative diagonal
maximize t
subject to 
t <= transpose(vec(W))*K*vec(W)
for ii=1:16

but it didn’t work. Can you help me?

It appears that K should really be indexed by i and j, and that you need a constraint for every i \ne j, yet you only have a single constraint involving K, and you do not show us what that K is.

You declared W as diagonal, yet the image has W' as well as W, which would seem strange if W is diagonal (which isn’t mentioned in the image).

There may be more wrong as well, but perhaps get started on this.

This is norm maximization and does not look convex.

Thank you for your prompt response. H is a channel matrix 4x4 and its values are given below:

H= 1e-5 * [0.6250 0.6101 0.5958 0.6101;
0.6101 0.6250 0.6101 0.5958;
0.5958 0.6101 0.6250 0.6101;
0.6101 0.5958 0.6101 0.6250]

K is a matris with 16x16 and it is calculated by

K = transpose(kron(H,D.’))*kron(H,D.’);

where D is (s_i-s_j) where s is the constellation point and its dimension is 120x4.

In the paper, it is stated that “The diagonal precoder can be obtained by solving the optimization problem in (12) with an additional constraint w_kl = 0 when k ̸= l.

The diagonal precoder
WD obtained by solving (12) is given by WD = diag{0.2154, 0.4290, 0.3568, 0.5}

I hope these info are useful to describe my problem.

Have you proven this is a convex optimization problem? Per the rules of the forum, a statement in a book or paper asserting convexity or solvability by CVX doesn’t count.

Thank you for your help. I try to prove it.


sorry to bother you ,i wanna ask do you know how to maximize an convex expression?the matlab shows it can’t maximize an convex expression…

You use a non-convex solver. And that probably is the case for your other question, Disciplined convex programming error: Cannot perform the operation: {complex affine} .* {log-affine} . So not CVX. You might be able to use YALMIP.

The only non-convex problems which can be handled in CVX are those for which the only non-convexity is binary or integer constraints on the variables.