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.

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-t*Q))>=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?