How to correct the code?

I have to maximize the objective function with respect to x1 and x2.

func = -(x2*(-10)-x1*70+3*(80))

%Constrains are

3<=x1 ; x2<=8

This optimization has to be done in penality function method.

But my code has not working.

clc
clear
format long      
syms x1 x2;
% objective function
func =  -(x2*(-10)-x1*70+3*(80));
%Constrains 
g1(1) = 3-x1;
g1(2) = x2-8;

eps = 0.001;
%initialize the convergance criteria
conv = 1;
% Initial Guess 
i = 1;
x_1(i) = 3;
x_2(i) = 8;
rk(1) =0.001;
% addition of penality factor
f = func - rk(1)*(g1(1)+g1(2))

f = 

k = 1;
while conv > eps
    Grad_f = gradient(f);
    S = -subs(Grad_f,[x1,x2],[x_1(i),x_2(i)])
 
    while norm(S)> eps
        %calculate the step length
        syms lambda
        func_lambda = subs(f, [x1,x2], [x_1(i)+S(1)*lambda,x_2(i)+lambda*S(2)])
        dfunc_lambda = (diff(func_lambda,lambda))
        lambda = vpa(solve(dfunc_lambda==0,lambda),6);
        lambda = lambda(imag(lambda)==0)
        for k = 1:size(lambda)
            fun_lambda_value(k) = subs(f,[x1,x2],[x_1(i)+lambda(k,1)*S(1),x_2(i)+lambda(k,1)*S(2)])
        end
        [value, index] = min(fun_lambda_value)
        %compute the step length
        lambda = lambda(index)
        %replace the old value with new value for unconstrained
        x_1(i+1) = x_1(i)+lambda*S(1)
        x_2(i+1) = x_2(i)+lambda*S(2)
        Grad_old = subs(Grad_f,[x1,x2],[x_1(i),x_2(i)])
        i = i+1
        Grad_new = subs(Grad_f,[x1,x2],[x_1(i),x_2(i)])
        %update the search direction
        S = -(Grad_new)+((norm(Grad_new))^2/(norm(Grad_old))^2)*S 
    end
    Phi1 = subs(func,[x1,x2],[x_1(i-1),x_2(i-1)])
    Phi2 = subs(func,[x1,x2],[x_1(i),x_2(i)])
    conv = abs(abs(Phi2)-abs(Phi1))/abs(Phi1)
    rk(k+1) = 0.01*rk(k)     
    k= k+1
end

S = 

func_lambda = 

dfunc_lambda = 

 
lambda =
 
Empty sym: 0-by-1
 

Unrecognized function or variable 'fun_lambda_value'.

Iter = 1:i;
K = 1:k
X_coordinate = x_1'
Y_coordinate = x_2'
Iterations = Iter'
Rk = rk'
for i=1:length(X_coordinate)
    Objective_value(i) = double(subs(f,[x1,x2], [x_1(i),x_2(i)]))
end
Objective_value = Objective_value'
T = table(Iterations,X_coordinate,Y_coordinate, Objective_value)

I can't understand this error.How to rectify it?How to change the lamba as a empty system?

note: In function, -10,70,80 are changeable values.

Answer 1

[Jan]

for k = 1:size(lambda)
   fun_lambda_value(k) = subs(f,[x1,x2],[x_1(i)+lambda(k,1)*S(1),x_2(i)+lambda(k,1)*S(2)])
end

If lamda is a [1 x N] row vector, "1:size(lambda)" means "1:[1,N]". The colon operator uses the first element only, if an argument is a vector.

You want instead:

for k = 1:numel(lambda)    

But in your case fun_lambda_value is not defined at all. Then lambda is empty and

[value, index] = min(fun_lambda_value)    

cannot work.

I assume, the code has another bug: If lambda is smaller than in the former iteration, only the first elements are overwritten. I assume you want to set fun_lambda_value to a default value before the loop.