I want to find the optimized vectors w_r and w_t jointly in the following problem.

where H is a known matrix with M * N dimensions, h_2 is an N * 1 known vector and h_1 is an M * 1 known vector.

Also, w_t is an N * 1 vector and w_r is an M * 1 vector; (.)^H denotes the hermitian operator.

Can the above problem be solved using CVX?

If yes? how?

It is worth noting that I wrote the objective function of the above problem in MATLAB as follows and received an error message.

cvx_begin

variable wt(N) complex % N is known parameter

variable wr(M) complex % M is known parameter

maximize min ( square_pos ( norm((h_2’ * wt),1) ) , square_pos ( norm((wr’ * h_1),1) ) )

cvx_end

% command window message:

Disciplined convex programming error:

Cannot perform the operation min( {convex}, {convex} )

Thank you in advance for your helps and suggestions.