Reputation: 25
I have a problem with my MATLAB code that I write to minimize this function with two constraints (one of them is inequality and the other one is equality) with Lagrange Multipliers that use KKT conditions. This the Function :
MIN F = 2*x1^2 + 2*x2^2-6*x1*x2
ineq=x1+2*x2<=3
eq=3*x1+x2=9
I am personally suspect that my if Function(statement) has problem but don't know how to fix that .....
clc
warning off
syms x1 x2 u s lambda
f=2*x1^2+2*x2^2-6*x1*x2;
g1=sqrt(x1^2*x2)+s^2-0.25;
H1=x1*x2^2-0.1;
Lagrange=f+u*g1+lambda*H1;
Grad=gradient(Lagrange);
S=solve(Grad);
S=double([S.x1 S.x2 S.s S.u S.lambda]);M=size(S,1);
for i=M:-1:1
if imag(S(i,3))~=0 || S(i,1)<=0 || S(i,2)<=0
end
end
x1=S(:,1);x2=S(:,2);s=S(:,3);u=S(:,4);lambda=S(:,5);
out=table(x1,x2,s,u,lambda)
x0=[1 0.5 -0.75];
It seems I have a problem because it gives me both write and wrong answers can you help me with that ?
Upvotes: 1
Views: 1558
Reputation: 2777
Just eliminate the corresponding row when if
condition is satisfied using S(i,:)=[];
According to your formulation
The if
condition should look like this
if imag(S(i,3))~=0 || S(i,1)<=0 || S(i,2)<=0
S(i,:)=[];
end
Solution
out =
1×5 table
x1 x2 s u lambda
______ _______ _ ______ _______
0.3393 0.54288 0 3.6349 -2.6402
From my point of view your equality and inequality constraints formulation are wrong
ineq = x1 + 2*x2 <= 3 -------> g1 = x1 + 2*x2 - 3 + s^2
eq = 3*x1 + x2 = 9 -------> H1 = 3*x1 + x2 - 9
The if
condition checks
u
(modifying g1
) is less than zero or not or
s
is real number or notfor i=M:-1:1
if imag(S(i,3))~=0 || S(i,4)<0
S(i,:)=[];
end
end
The entire code is as follow
syms x1 x2 u s lambda
f=2*x1^2+2*x2^2-6*x1*x2;
g1 = x1+2*x2-3 +s^2 ;
H1 = 3*x1+x2-9;
Lagrange=f+u*g1+lambda*H1;
Grad=gradient(Lagrange);
S=solve(Grad)
S=double([S.x1 S.x2 S.s S.u S.lambda]);M=size(S,1)
for i=M:-1:1
if imag(S(i,3))~=0 || S(i,4)<0
S(i,:)=[];
end
end
x1=S(:,1);x2=S(:,2);s=S(:,3);u=S(:,4);lambda=S(:,5);
out=table(x1,x2,s,u,lambda)
Solution
out =
1×5 table
x1 x2 s u lambda
__ __ _ ____ ______
3 0 0 13.2 -8.4
Check your answer using
fmincon
as follow
% Check your answer using fmincon
% Inequality constraint
%ineq = x1 + 2*x2 <= 3
A = [1, 2];
b = 3;
% Equality constraint
%eq = 3*x1 + x2 = 9
Aeq = [3, 1];
beq = 9;
%F = 2*x1^2 + 2*x2^2-6*x1*x2
F = @(x)2*x(1).^2 + 2*x(2).^2-6*x(1).*x(2);
x0 = [0,0];
[x_minimum, Feval] = fmincon(F, x0, A, b, Aeq, beq);
Solution
x_minimum =
3.0000 -0.0000
Feval =
18.0002
Upvotes: 1