problems with fmincon, how to solve?

can someone help me solve this problem, I tried to modify the code but it didn't solve it. I need to minimize the following equation.

objective function:

function cosmyfun(x)
cost = @(x) dfghjhgfx(1)^2 + x(2)^2 - 5*x(1) - 6*x(2) + 15;
end

function with restrictions of inequality and equality:

function [c,ceq]=mycon(x)
c(1) = x(1)^2 + x(2)^2 - 4*x(1) - 3*x(2) + 5;
c(2) = -x(1)^2 - x(2)^2 + 4*x(1) + 3*x(2) - 10; 
ceq = 2*x(1)^2 + 2*x(2)^2 - 3*x(1) - 3*x(2) - 2; 
end

script:

clc
clear all
Aeq=[]; 
beq=[]; 
A=[]; 
b=[]; 
lb=[-3,-3]; 
ub=[3,3]; 
x0=[4,4];
options = optimoptions('fmincon','Algorithm','sqp','Display','iter-detailed','MaxFunctionEvaluations',100000, 'MaxIterations',2000, 'OptimalityTolerance' ,1e-10);
[x,cost] = fmincon(@(x) myfun,x0,A,b,Aeq,beq,lb,ub,mycon)

error:

Error in mycon (line 2)

c(1) = x(1)^2 + x(2)^2 - 4*x(1) - 3*x(2) + 5;

Error in Example (line 11)

[x,cost] = fmincon(@(x) myfun,x0,A,b,Aeq,beq,lb,ub,mycon)

Answer 1

[Hussein Ammar]

Your problem is convex, so you can use the CVX package if you want. Also, the solution should be the global minimum; not a local minimum. To use fmincon, do the following:

Equality/nonEquality constraint:

function [c,ceq]=mycon(x)
c(1) = x(1)^2 + x(2)^2 - 4*x(1) - 3*x(2) + 5;
c(2) = -x(1)^2 - x(2)^2 + 4*x(1) + 3*x(2) - 6; % notice the fixed typo
ceq = 2*x(1)^2 + 2*x(2)^2 - 3*x(1) - 3*x(2) - 2; 
end

Construct the problem and call fmincon:

clc
clear all
Aeq=[]; 
beq=[]; 
A=[]; 
b=[]; 
% if you are not sure that vector x is within lb and ub do not restrict it
lb = []; %lb=[-3,-3]; 
ub = []; %ub=[3,3]; % 
x0=[4,4];
myObj = @(x) x(1)^2 + x(2)^2 - 5*x(1) - 6*x(2) + 15;
nonlcon = @mycon;

options = optimoptions('fmincon','Algorithm','sqp','Display','iter-detailed','MaxFunctionEvaluations',100000, 'MaxIterations',2000, 'OptimalityTolerance' ,1e-10);
[x,cost] = fmincon(myObj,x0,A,b,Aeq,beq,lb,ub,nonlcon)

Output (global minimum):

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.

<stopping criteria details>

x =

    1.6450    1.9007


cost =

    1.6896