Please help me in writing the cvx program for the following problem:
max t
s.t trace(X*(R-tQ))>=sigma*t
and X_ii<=P_i/D_ii
and X>=0;
X(r,r) and t are the variables, R,Q,sigma,P,D are known variables.
Read section 4.2.5 “Quasiconvex optimization” of “Convex Optimization” by Boyd and Vandenberghe http://web.stanford.edu/~boyd/cvxbook/
Yes, the problem can be formulated as a feasibility problem by assigning t some value. But the problem comes in writing the first set of constraint in cvx.
ie. trace(X*(R-tQ))>=sigma t
where R,t,Q,sigma are known.
Did you also read section 3.4.5, which is referenced in section 4.2.5?