117 lines
4.8 KiB
Matlab
117 lines
4.8 KiB
Matlab
% Define environment (functions, gradients etc...)
|
|
GivenEnv
|
|
|
|
% Define parameters
|
|
max_iter = 300; % Maximum iterations
|
|
tol = 1e-4; % Tolerance
|
|
|
|
% Point x0 = (0, 0)
|
|
% =========================================================================
|
|
point = 1;
|
|
x0 = [0, 0];
|
|
f = fun(x0(1), x0(2));
|
|
gf = grad_fun(x0(1), x0(2));
|
|
hf = hessian_fun(x0(1), x0(2));
|
|
fprintf('Initial point (%d, %d), f = %f, grad = [%f;%f], hessian = [%f %f ; %f %f]. Can NOT use method\n', x0, f, gf, hf);
|
|
disp(' ');
|
|
|
|
|
|
% Point x0 = (-1, 1)
|
|
% =========================================================================
|
|
point = 2;
|
|
x0 = [-1, 1];
|
|
point_str = "[" + x0(1) + ", " + x0(2) + "]";
|
|
|
|
f = fun(-1, 1);
|
|
gf = grad_fun(x0(1), x0(2));
|
|
hf = hessian_fun(x0(1), x0(2));
|
|
fprintf('Initial point (%d, %d), f = %f, grad = [%f;%f], hessian = [%f %f ; %f %f]. Can use method\n', x0, f, gf, hf);
|
|
|
|
% Find the best fixed gamma
|
|
k = zeros(100, 1);
|
|
j = 1;
|
|
n = linspace(0.1, 1.5, 100);
|
|
for g = n
|
|
gamma_fixed_step = g;
|
|
[~, ~, k(j)] = method_steepest_descent(fun, grad_fun, x0, tol, max_iter, 'fixed');
|
|
j = j + 1;
|
|
end
|
|
plotItersOverGamma(n, k, "Iteration for different $\gamma$ values", "figures/StDes_Iter_o_gamma_" + point + ".png");
|
|
|
|
[~, j] = min(k);
|
|
gamma_fixed_step = n(j);
|
|
|
|
[x_fixed, f_fixed, kk] = method_steepest_descent(fun, grad_fun, x0, tol, max_iter, 'fixed');
|
|
fprintf('Fixed step: Initial point (%f, %f), steps:%d, Final (x,y)=(%f, %f), f(x,y)=%f\n', x0, kk, x_fixed(end, :), f_fixed(end));
|
|
plotPointsOverContour(x_fixed, fun, [-2, 0], [-2, 2], 100, point_str + ": Steepest descent $\gamma$ = " + gamma_fixed_step, "figures/StDes_fixed_" + point + ".png");
|
|
|
|
|
|
% Minimized f
|
|
[x_minimized, f_minimized, kk] = method_steepest_descent(fun, grad_fun, x0, tol, max_iter, 'minimized');
|
|
fprintf('Minimized f(g): Initial point (%f, %f), steps:%d, Final (x,y)=(%f, %f), f(x,y)=%f\n', x0, kk, x_minimized(end, :), f_minimized(end));
|
|
plotPointsOverContour(x_minimized, fun, [-2, 0], [-2, 2], 100, point_str + ": Steepest descent minimized $f(x_k + \gamma_kd_k)$", "figures/StDes_minimized_" + point + ".png");
|
|
|
|
|
|
% Armijo Rule
|
|
|
|
% Methods tuning
|
|
amijo_beta = 0.4; % typical range: [0.1, 0.8]
|
|
amijo_sigma = 0.1; % typical range: [0.01, 0.3]
|
|
|
|
[x_armijo, f_armijo, kk] = method_steepest_descent(fun, grad_fun, x0, tol, max_iter, 'armijo');
|
|
fprintf('Armijo step: Initial point (%f, %f), steps:%d, Final (x,y)=(%f, %f), f(x,y)=%f\n', x0, kk, x_armijo(end, :), f_armijo(end));
|
|
plotPointsOverContour(x_armijo, fun, [-2, 0], [-2, 2], 100, point_str + ": Steepest descent Armijo method", "figures/StDes_armijo_" + point + ".png");
|
|
disp(' ');
|
|
|
|
% Compare methods
|
|
plotConvCompare(x_fixed, "Fixed", x_minimized, "Minimized", x_armijo, "Armijo", Xmin, "Convergence compare", "figures/StDes_compare_" + point + ".png");
|
|
|
|
% Point x0 = (1, -1)
|
|
% =========================================================================
|
|
point = 3;
|
|
x0 = [1, -1];
|
|
point_str = "[" + x0(1) + ", " + x0(2) + "]";
|
|
|
|
f = fun(-1, 1);
|
|
gf = grad_fun(x0(1), x0(2));
|
|
hf = hessian_fun(x0(1), x0(2));
|
|
fprintf('Initial point (%d, %d), f = %f, grad = [%f;%f], hessian = [%f %f ; %f %f]. Can use method\n', x0, f, gf, hf);
|
|
|
|
% Find the best fixed gamma
|
|
k = zeros(100, 1);
|
|
j = 1;
|
|
n = linspace(0.1, 1, 100);
|
|
for g = n
|
|
gamma_fixed_step = g;
|
|
[~, ~, k(j)] = method_steepest_descent(fun, grad_fun, x0, tol, max_iter, 'fixed');
|
|
j = j + 1;
|
|
end
|
|
%if min(k) == max_iter
|
|
% fprintf('Fixed step: Initial point (%d, %d). Can NOT use method\n', x0);
|
|
%end
|
|
%plotItersOverGamma(n, k, "Iteration for different $\gamma$ values", "figures/StDes_Iter_o_gamma_" + point + ".png");
|
|
|
|
%gamma_fixed_step = 1;
|
|
[x_fixed, f_fixed, kk] = method_steepest_descent(fun, grad_fun, x0, tol, max_iter, 'fixed');
|
|
fprintf('Fixed step: Initial point (%f, %f), steps:%d, Final (x,y)=(%f, %f), f(x,y)=%f\n', x0, kk, x_fixed(end, :), f_fixed(end));
|
|
plotPointsOverContour(x_fixed, fun, [-1, 2], [-2, 2], 100, point_str + ": Steepest descent $\gamma$ = " + gamma_fixed_step, "figures/StDes_fixed_" + point + ".png");
|
|
|
|
|
|
% Minimized f
|
|
[x_minimized, f_minimized, kk] = method_steepest_descent(fun, grad_fun, x0, tol, max_iter, 'minimized');
|
|
fprintf('Minimized f(g): Initial point (%f, %f), steps:%d, Final (x,y)=(%f, %f), f(x,y)=%f\n', x0, kk, x_minimized(end, :), f_minimized(end));
|
|
plotPointsOverContour(x_minimized, fun, [-2, 2], [-3, 2], 100, point_str + ": Steepest descent minimized $f(x_k + \gamma_kd_k)$", "figures/StDes_minimized_" + point + ".png");
|
|
|
|
|
|
% Armijo Rule
|
|
|
|
% Methods tuning
|
|
amijo_beta = 0.4; % typical range: [0.1, 0.8]
|
|
amijo_sigma = 0.1; % typical range: [0.01, 0.3]
|
|
|
|
[x_armijo, f_armijo, kk] = method_steepest_descent(fun, grad_fun, x0, tol, max_iter, 'armijo');
|
|
fprintf('Armijo step: Initial point (%f, %f), steps:%d, Final (x,y)=(%f, %f), f(x,y)=%f\n', x0, kk, x_armijo(end, :), f_armijo(end));
|
|
plotPointsOverContour(x_armijo, fun, [-1, 2], [-2, 2], 100, point_str + ": Steepest descent Armijo method", "figures/StDes_armijo_" + point + ".png");
|
|
|
|
|