Fmincon failure in optimizing an objective function which includes determinant of a matrix.

Here, fmincon is not working with the below mentioned objective function, and same was working when i was finding the frobenious norm of the matrix. Can someone please help me out in this?

Nr=4;No=1;
N = 4;
h = sqrt(0.5)*(randn(N,N)+1i*randn(N,N));
g = sqrt(0.5)*(randn(N,N)+1i*randn(N,N));

phi0 = zeros(N,1);
lb = zeros(N,1);
ub = 2*pi*ones(N,1);

obj = @(phi)-det(eye(Nr)+((g*diag(exp(1i*phi))*h)*(g*diag(exp(1i*phi))*h)')/No);
[sol,~] = fmincon(obj,phi0,[],[],[],[],lb,ub);

Error using barrier
Objective function is undefined at initial point. Fmincon cannot continue.

Error in fmincon (line 886)
[X,FVAL,EXITFLAG,OUTPUT,LAMBDA,GRAD,HESSIAN] = barrier(funfcn,X,A,B,Aeq,Beq,l,u,confcn,options.HessFcn, ...

Answer 1

[Bruno Luong]

Make sure your objective function returns real numerical output

Nr=4;No=1;
N = 4;
h = sqrt(0.5)*(randn(N,N)+1i*randn(N,N));
g = sqrt(0.5)*(randn(N,N)+1i*randn(N,N));
phi0 = zeros(N,1);
lb = zeros(N,1);
ub = 2*pi*ones(N,1);
obj = @(phi)-det(eye(Nr)+real(((g*diag(exp(1i*phi))*h)*(g*diag(exp(1i*phi))*h)'))/No);

[sol,~] = fmincon(obj,phi0,[],[],[],[],lb,ub);

Local minimum possible. Constraints satisfied.

fmincon stopped because the size of the current step is less than
the value of the step size tolerance and constraints are 
satisfied to within the value of the constraint tolerance.

[Shankul Saini]

okay, thanks @Bruno Luong for pointing out.