Solver not applicable for a quadratic cost function subject to a set of LMIs

[Li Li]

Hi John,

I tried to solve an optimization problem involving a quadratic cost function subject to a set of LMIs. I used different Quadratic programming solvers, e.g. gurobi, QPIP, QPAS, and it gave the error message "Solver not applicable". The code is as follows. Could you please help me out? Thanks

Regards

Li

X1 = sdpvar(6,6,'symmetric');

X6 = sdpvar(6,6,'symmetric');

F1 = sdpvar(6,6,'full');

bet  = sdpvar(1,1);

x = [bet>0 ];

x= [x, [(A1+alpha*eye(6))'*X1+X1*(A1+alpha*eye(6))-F1-F1'-C21'*E21*C21+2* ...

bet*eye(6) X1*B20; B20'*X1 -eye(8)]<0];

x= [x, [alpha*X1 bet*eye(6)-F1; bet*eye(6)-F1' alpha*X6]>0];

x= [x, [rho*X1 F1'; F1 X1]>0];

obj = -bet/6-p_bet*bet+c_update/2*(bet-bet_fusion)*(bet-bet_fusion);

obj = obj -trace(P_X1'*X1)+c_update/2*trace((X1-X_fusion1)'*(X1-X_fusion1));

obj = obj -trace(P_X6'*X6)+c_update/2*trace((X6-X_fusion6)'*(X6-X_fusion6));

sol=solvesdp(x,obj,sdpsettings('solver','gurobi'));

[Johan Löfberg]

All those solvers are for quadratic programs. You obviously have a semidefinite program.