Solving an optimization problem using fmincon

Can anyone help me to solve this? I do not know how to use the contraint on C3 and how to implement ri in it!

Answer 1

[Alan Weiss]

I think that this is a straightforward problem is you use the problem-based optimization workflow, which requires a relatively recent version of Optimization Toolbox™.

Alan Weiss

MATLAB mathematical toolbox documentation

[Behzad Eydiyoon]

thank you for the reply

I wrote this code for it

clc
clear
close all
prob = optimproblem('ObjectiveSense','min');
x = optimvar('x',3,1,'LowerBound',0,'UpperBound',inf);
i=[1:3];
j=[1:3];
a=rand(3,1);
a1=diag(a)';
r=rand(3,1);
cons1 = sum(x(i)) <= 10;
cons2 = sum(r(i).*x(i)) >= 10;

prob.Constraints.cons1 = cons1;
prob.Constraints.cons2 = cons2;

prob.Objective = sum(sum(a1(i,j),2).*x(i).*x(j));
[sol,fval] = solve(prob);
disp(sol.x)
disp(fval)

seems to be okay. it worked but also it said : "quadprog stopped because it was unable to find a point that satisfies the constraints within the value of the constraint tolerance"

[Alan Weiss]

So you were able to program it. Good for you!

Now let's look at your constraints:

cons1 = sum(x) <= 10;
cons2 = sum(r.*x) >= 10;

The r variable has all entries between 0 and 1, and the x variable is nonnegative. Therefore, for any x satisfying cons1, the value of sum(r.*x) is smaller. Therefore your constraints are inconsistent.

Alan Weiss

MATLAB mathematical toolbox documentation

[Behzad Eydiyoon]

you are right!

thank you a lot.