Help with 'fmincon' fucntion for optimsation

Hi,

I am trying to find the minimum value of the function with fmincon, but i need some help. My code is written here.

clc

m = 8;
a =[.75,0.75,0.85,0.8];

x0 = [0,0,0,0];
lb = [0,0,0,0];
ub = [5,2,4,5];
nonlincon = @nlcon;

objective = @(x) (x(1)*a(1))+(x(2)*a(2))+(x(3)*x(3))+(x(4)*a(4));

[i,fval] = fmincon(objective,x0,[],[],[],[],lb,ub,nonlincon);

Local minimum found that satisfies the constraints.

Optimization completed because the objective function is non-decreasing in 
feasible directions, to within the value of the optimality tolerance,
and constraints are satisfied to within the value of the constraint tolerance.

disp(i)

    4.2066    1.4184    0.3750    0.0000

fval

fval = 4.3594

function [c,ceq] = nlcon(x)
c = [];
ceq = sum(x)-6;
end

1. I need to include the variable (m) into nlcon fucntion and use it instead of 6. I tried different ways and its not working. I hope some of you can help me with this.
2. The minimum value from the program is wrong. If you multiply (x*a), you would see fval = 4.53. But the result shows 4.359. Also the minimum possible fval = 4.5, when x1 = 4.5 and x2 = 1.5. How can i make this correct?

I really appreciate your help on this one. Thank you in advance :).

Answer 1

[Torsten]

Your problem is linear. You might want to try "linprog" instead of "fmincon".

m = 6;
a =[.75,0.75,0.85,0.8];
x0 = [0,0,0,0];
lb = [0,0,0,0];
ub = [5,2,4,5];
Aeq = [1 1 1 1];
beq = m;
objective = @(x) (x(1)*a(1))+(x(2)*a(2))+(x(3)*a(3))+(x(4)*a(4));
[i,fval] = fmincon(objective,x0,[],[],Aeq,beq,lb,ub)

Local minimum found that satisfies the constraints.

Optimization completed because the objective function is non-decreasing in 
feasible directions, to within the value of the optimality tolerance,
and constraints are satisfied to within the value of the constraint tolerance.

i = 1×4

4.3430 1.6570 0.0000 0.0000

fval = 4.5000

[Shemin Sagaria]

Thank you very much ;)