OM/Claudio_Maggioni_5/main.m

clc
clear
close all

%% Exercise 2.1

syms x1 x2
c1 = 2 * x1 + 3 * x2 - 6;
c2 = -3 * x1 + 2 * x2 - 3;
c3 = 2 * x2 - 5;
c4 = 2 * x1 + x2 - 4;

c1 = solve(c1 == 0, x2, 'Real', true);
c2 = solve(c2 == 0, x2, 'Real', true);
c3 = solve(c3 == 0, x2, 'Real', true);
c4 = solve(c4 == 0, x2, 'Real', true);

i1 = solve(c1 == c2, x1, 'Real', true);
i2 = solve(c1 == c4, x1, 'Real', true);
i3 = solve(c4 == 0, x1, 'Real', true);

px = double([0 0 i1 i2 i3]);
pysym = [0 subs(c2, x1, 0) subs(c1, x1, i1) subs(c4, x1, i2) subs(c4, x1, i3)];
py = double(pysym); 

xl = -0.05;
xh = 2.05;

orange = [232/255 128/255 18/255];
grey = [0.5 0.5 0.5];
colors = [orange; 0 0 1; 1 0 0; 0 1 0];
dirs = [30 30 30 30];

axis([-0.05 2.05 -0.15 5.15])
i = 1;
hold on
for c = [c1 c2 c3 c4]
    pl = patch([xl, xl, xh, xh], ...
      double([-0.15, subs(c, x1, xl), subs(c, x1, xh), -0.15]), ...
      colors(i, :));
    pl.EdgeColor = colors(i, :);
    pl.FaceAlpha = .2;
    pl.EdgeAlpha = .2;
    i = i + 1;
end

pl = patch([0, 0, xh, xh], ...
              double([0, 5.15, 5.15, 0]), ...
              grey);
pl.EdgeColor = grey;
pl.FaceAlpha = .2;
pl.EdgeAlpha = .2;

pl = patch(px, py, 'green');
pl.EdgeColor = 'green';

legend('2x1 + 3x2 <= 6', '-3x1 + 2x2 <= 3', '2x2 <= 5', ...
    '2x1 + x2 <= 4', 'x1 > 0 and x2 > 0', 'feasible region');
hold off

%% Exercise 3.1

G = [6 2 1; 2 5 2; 1 2 4];
c = [-8; -3; -3];
A = [1 0 1; 0 1 1];
b = [3; 0];

K = [G A'; A zeros(2)];
eig(K)

%% Exercise 3.2

[x, lambda] = uzawa(G, c, A, b, [0;0;0], [0;0], 1e-8, 100);
display(x);
display(lambda);