Object objective function influences whether my problem is feasible.

[Peng He]

Hi:

    I want to solve a SDP program using YALMIP. And my code is

function [alpha,x,eta1,eta2,Q,W] = rand_test(N,mu,Sigma,r0,beta,gamma1,gamma2)

%varibles

alpha = sdpvar(1);

lambda1 = sdpvar(1);

kama1 = sdpvar(1);

eta1 = sdpvar(N,1);

eta2 = sdpvar(N,1);

tao1 = sdpvar(N,1);

tao2 = sdpvar(N,1);

x = sdpvar(N,1);

Q = sdpvar(N,N);

W = sdpvar(N,N);

%constraints

c1 = [eta1 >= 0];

c2 = [eta2 >= 0];

c3 = [tao1 >= 0];

c4 = [tao2 >= 0];

c5 = [Q >= 0];%Semidefinite constraint

c6 = [W >= 0];%Semidefinite constraint

c7 = [x >= 0];

c8 = [sum(x)==1];

c9 = [[Q (eta1-eta2+x)/2-Q*mu;((eta1-eta2+x)/2-Q*mu)' lambda1+alpha]>=0];%Semidefinite constraint

c10 = [[Q (eta1-eta2)/2-Q*mu;((eta1-eta2)/2-Q*mu)' lambda1]>=0];%Semidefinite constraint

c11 = [[W (tao1-tao2+x)/2-W*mu;((tao1-tao2+x)/2-W*mu)' kama1]>=0];%Semidefinite constraint

c12 = [-kama1-tao1'*(mu+gamma1)+tao2'*(mu-gamma1)-sum(sum(W.*(gamma2*Sigma-mu*mu')))>=r0];

%c13 = [lambda1 >= 0];

%c14 = [kama1 >= 0];

Constraints = [c1,c2,c3,c4,c5,c6,c7,c8,c9,c10,c11,c12];

%object

Obj = alpha+1/(1-beta)*(lambda1+eta1'*(gamma1+mu)+eta2'*(gamma1-mu)+sum(sum(Q.*(gamma2*Sigma-mu*mu'))));

optimize(Constraints);% Problem status  : PRIMAL_AND_DUAL_FEASIBLE;  Solution status : OPTIMAL
optimize(Constraints,Obj);% Problem status  : PRIMAL_INFEASIBLE ; Solution status : PRIMAL_INFEASIBLE_CER

%solvesdp(Constraints);

check(Constraints)在此输入代码...

When I execute ‘optimize’ function without objective function,there's a optimal solution,but when execute the same function with objective function,the problem status turns out 'The problem is primal infeasible'.I'm confused,why objective function can influence feasible region?Thanks.

[Johan Löfberg]

That typically means the problem is unbounded (dual unbounded/primal infeasible)

Simple trick is to add constraints Obj >= -10000 for example, and solve. If the solution nicely ends up at -10000, you should suspect unbounded. Look at the values at that point, most likely you will see that some variables tend to very large values, i.e., you've formulated a bad model missing constraints

[Peng He]

Many thanks.I'll check my model again.