matlab exercise program (quadratic programming - Lagrangian method)

Recently read quadratic programming method for equality constrained quadratic programming problems can be solved using Lagrangian method.

The derivation method "Optimization Theory and Algorithms (2nd Edition)" of the book:

Here the following codes (the code given three examples):

clear all;
close all;
clc;

% min     x1^2+2*x2^2+x3^2+x2^2-2*x1*x2+x3
% s.t.    x1+x2+x3 = 4
%         2*x1-x2+x3 = 2
%{
H=[2 -2 0;
   -2 4 0;
   0 0 2];
c = [0 0 1]';
A=[1 1 1;
   2 -1 1];
b=[4 2]';
%}

%min      2*x1^2+x2^2+x1*x2-x1-x2  
%s.t.     x1+x2 = 1
H=[4 1;
   1 2];
c=[-1 -1]';
A=[1 1];
b=1;

%min    1.5*x1^2-x1*x2+x2^2-x2*x3+0.5*x3^2+x1+x2+x3
%s.t.   x1+2*x2+x3 = 4
%{
H=[3 -1 0;
   -1 2 -1;
   0  -1 1];
c=[1 1 1]';
A=[1 2 1];
b=4;
%}

invH = inv(H);
S = -inv(A*invH*A');
R = -S*A*invH;
Q = invH-invH*A'*R;
x = -Q*c+R'*b;

[x1,x2]=meshgrid(0:0.02:0.7,0:0.02:1.5);
z1 = 2*x1.^2+x2.^2+x1.*x2-x1-x2;
mesh(x1,x2,z1);

x1 = 0:0.02:0.7;
x2 = -x1 + 1;

hold on;
plot3(x1,x2,zeros(1,length(x1)),'r');
plot3(x(1),x(2),0,'r*')
plot3(x(1),x(2),2*x(1).^2+x(2).^2+x(1).*x(2)-x(1)-x(2),'b*')

结果如下：

图中红线为约束条件，曲面为待求解问题函数，红点为问题的解，蓝点为二次规划问题最小值所在的位置。