77 lines
1.5 KiB
Matlab
77 lines
1.5 KiB
Matlab
clc
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clear
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close all
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%% Exercise 2.1
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syms x1 x2
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c1 = 2 * x1 + 3 * x2 - 6;
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c2 = -3 * x1 + 2 * x2 - 3;
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c3 = 2 * x2 - 5;
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c4 = 2 * x1 + x2 - 4;
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c1 = solve(c1 == 0, x2, 'Real', true);
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c2 = solve(c2 == 0, x2, 'Real', true);
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c3 = solve(c3 == 0, x2, 'Real', true);
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c4 = solve(c4 == 0, x2, 'Real', true);
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i1 = solve(c1 == c2, x1, 'Real', true);
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i2 = solve(c1 == c4, x1, 'Real', true);
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i3 = solve(c4 == 0, x1, 'Real', true);
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px = double([0 0 i1 i2 i3]);
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pysym = [0 subs(c2, x1, 0) subs(c1, x1, i1) subs(c4, x1, i2) subs(c4, x1, i3)];
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py = double(pysym);
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xl = -0.05;
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xh = 2.05;
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orange = [232/255 128/255 18/255];
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grey = [0.5 0.5 0.5];
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colors = [orange; 0 0 1; 1 0 0; 0 1 0];
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dirs = [30 30 30 30];
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axis([-0.05 2.05 -0.15 5.15])
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i = 1;
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hold on
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for c = [c1 c2 c3 c4]
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pl = patch([xl, xl, xh, xh], ...
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double([-0.15, subs(c, x1, xl), subs(c, x1, xh), -0.15]), ...
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colors(i, :));
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pl.EdgeColor = colors(i, :);
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pl.FaceAlpha = .2;
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pl.EdgeAlpha = .2;
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i = i + 1;
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end
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pl = patch([0, 0, xh, xh], ...
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double([0, 5.15, 5.15, 0]), ...
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grey);
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pl.EdgeColor = grey;
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pl.FaceAlpha = .2;
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pl.EdgeAlpha = .2;
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pl = patch(px, py, 'green');
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pl.EdgeColor = 'green';
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legend('2x1 + 3x2 <= 6', '-3x1 + 2x2 <= 3', '2x2 <= 5', ...
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'2x1 + x2 <= 4', 'x1 > 0 and x2 > 0', 'feasible region');
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hold off
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%% Exercise 3.1
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G = [6 2 1; 2 5 2; 1 2 4];
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c = [-8; -3; -3];
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A = [1 0 1; 0 1 1];
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b = [3; 0];
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K = [G A'; A zeros(2)];
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eig(K)
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%% Exercise 3.2
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[x, lambda] = uzawa(G, c, A, b, [0;0;0], [0;0], 1e-8, 100);
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display(x);
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display(lambda);
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