Unable to use for loop in fmincon

I am trying to maximize an expression using fmincon, which has 8 parameters, and an extra variable(p) which I want to keep as a parameter not to be used in maximization.

I have defined an objective function as shown below:

function fval = myfun1(K)
%define parameters
syms theta [1 4] real
syms phi [1 4] real
syms p real
theta1 = K(1);
theta2 = K(2);
theta3 = K(3);
theta4 = K(4);
phi1 = K(5);
phi2 = K(6);
phi3 = K(7);
phi4 = K(8);
% define eigenstates
psi_01 = [(1/2)*(1+cos(theta1))*exp(-1i*phi1); sqrt(1/2)*sin(theta1); (1/2)*(1-cos(theta1))*exp(1i*phi1)];
psi_02 = [(1/2)*(1+cos(theta2))*exp(-1i*phi2); sqrt(1/2)*sin(theta2); (1/2)*(1-cos(theta2))*exp(1i*phi2)];
psi_03 = [(1/2)*(1+cos(theta3))*exp(-1i*phi3); sqrt(1/2)*sin(theta3); (1/2)*(1-cos(theta3))*exp(1i*phi3)];
psi_04 = [(1/2)*(1+cos(theta4))*exp(-1i*phi4); sqrt(1/2)*sin(theta4); (1/2)*(1-cos(theta4))*exp(1i*phi4)];
psi_11 = [-sqrt(1/2)*sin(theta1)*exp(-1i*phi1); cos(theta1); sqrt(1/2)*sin(theta1)*exp(1i*phi1)];
psi_12 = [-sqrt(1/2)*sin(theta2)*exp(-1i*phi2); cos(theta2); sqrt(1/2)*sin(theta2)*exp(1i*phi2)];
psi_13 = [-sqrt(1/2)*sin(theta3)*exp(-1i*phi3); cos(theta3); sqrt(1/2)*sin(theta3)*exp(1i*phi3)];
psi_14 = [-sqrt(1/2)*sin(theta4)*exp(-1i*phi4); cos(theta4); sqrt(1/2)*sin(theta4)*exp(1i*phi4)];
psi_21 = [(1/2)*(1-cos(theta1))*exp(-1i*phi1); -sqrt(1/2)*sin(theta1); (1/2)*(1+cos(theta1))*exp(1i*phi1)];
psi_22 = [(1/2)*(1-cos(theta2))*exp(-1i*phi2); -sqrt(1/2)*sin(theta2); (1/2)*(1+cos(theta2))*exp(1i*phi2)];
psi_23 = [(1/2)*(1-cos(theta3))*exp(-1i*phi3); -sqrt(1/2)*sin(theta3); (1/2)*(1+cos(theta3))*exp(1i*phi3)];
psi_24 = [(1/2)*(1-cos(theta4))*exp(-1i*phi4); -sqrt(1/2)*sin(theta4); (1/2)*(1+cos(theta4))*exp(1i*phi4)];
%define projectors
P_01 = psi_01*psi_01';
P_02 = psi_02*psi_02';
P_03 = psi_03*psi_03';
P_04 = psi_04*psi_04';
P_11 = psi_11*psi_11';
P_12 = psi_12*psi_12';
P_13 = psi_13*psi_13';
P_14 = psi_14*psi_14';
P_21 = psi_21*psi_21';
P_22 = psi_22*psi_22';
P_23 = psi_23*psi_23';
P_24 = psi_24*psi_24';
%define the state in question
psi1 = (1/sqrt(3))*[1;0;0;0;1;0;0;0;1];
rho = p*(psi1*psi1') + (1-p)*(1/9)*kron(eye(3),eye(3));
% define the expression to maximize
P1 =  trace(rho*(kron(P_01,P_03)))+ trace(rho*(kron(P_11,P_13)))+trace(rho*(kron(P_21,P_23)));
P2 =  trace(rho*(kron(P_02,P_13)))+ trace(rho*(kron(P_12,P_23)))+trace(rho*(kron(P_22,P_03)));
P3 =  trace(rho*(kron(P_02,P_04)))+ trace(rho*(kron(P_12,P_14)))+trace(rho*(kron(P_22,P_24)));
P4 =  trace(rho*(kron(P_01,P_04)))+ trace(rho*(kron(P_11,P_14)))+trace(rho*(kron(P_21,P_24)));
P5 =  trace(rho*(kron(P_01,P_13)))+ trace(rho*(kron(P_11,P_23)))+trace(rho*(kron(P_21,P_03)));
P6 =  trace(rho*(kron(P_02,P_03)))+ trace(rho*(kron(P_12,P_13)))+trace(rho*(kron(P_22,P_23)));
P7 =  trace(rho*(kron(P_02,P_14)))+ trace(rho*(kron(P_12,P_24)))+trace(rho*(kron(P_22,P_04)));
P8 =  trace(rho*(kron(P_11,P_04)))+ trace(rho*(kron(P_21,P_14)))+trace(rho*(kron(P_01,P_24)));
fval = -real(P1+P2+P3+P4-P5-P6-P7-P8); % consider minus to maximize this function
end

I want to maximize the objective function fval for different values of p, ranging from 0 to 1. For a fixed value of p, I am able to maximize the function. However, I am unable to add a for loop to vary p.

The code for optimization is:

% variable bounds
lb = [0,0,0,0,0,0,0,0];
ub = [2*pi,2*pi,2*pi,2*pi,pi,pi,pi,pi];
for p = 0:0.2:1
        objective = @myfun1;
        % initial guess
        x0 = [0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5];
        % show initial objective
        disp(['Initial Objective: ' num2str(-objective(x0))])
        x = fmincon (objective,x0,[],[],[],[],lb,ub,[]);
        x
        % show final objective
        num2str(-objective(x))
end

Myfun1 is not considering the p values of the for loop defined above. Any help would be greatly appreciated.

Answer 1

[Alan Weiss]

You are not passing the value of p into myfun1. What is it supposed to represent in your code? What I mean is, when you write

for p = 0:0.2:1
    objective = @myfun1;

your objective does not depend on the value of p.

Alan Weiss

MATLAB mathematical toolbox documentation

[Ijaz Ahamed Mohammad]

Okay, I get it. How do I pass value of p using a for loop, so that I can maximize for various values of p? When I fix a value for the variable p, say, p = 0.1 in myfun1 and remove the for loop before using fmincon, I am able to maximize without any problems. But I would like maximize my 'fval' of myfun1 (which also depends on p) for different values of p and plot the maximum values for different p. I don't want 'p' to be a parameter which is used for maximization. Can you please guide me how I can achieve this?

[Alan Weiss]

As explaned in Passing Extra Parameters, write your function as a function of two variables, and then set one variable in the loop:

for p = 0:0.2:1
    objective = @(K)myfun1(K,p);
    % The rest of your optimization call here

Alan Weiss

MATLAB mathematical toolbox documentation

[Ijaz Ahamed Mohammad]

Got it! Thank you very much.