I need to solve a fitting problem and solve X according to the conditions Y =A*X. Y is a M*1 complex vector ,A is a M*N complex Dictionary Matrix，X is a N*1 complex vector. I want normalized X tend to be 0 or 1 by minimize ||x/max(x)-0.5||∞

cvx_begin

minimize( square_pos(norm(Y-A*X),2)+ lambda*norm((X*inv_pos(max(abs(X)))-0.5),inf))

cvx_end

matlab gives messages error using

I think it is because the object inside inv_pos need to be concave,but max(X) is convex. Then how can i rewrite the normalized X？

Please help me!