55 lines
2.1 KiB
Matlab
55 lines
2.1 KiB
Matlab
% Define environment (functions, gradients etc...)
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GivenEnv
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% Define parameters
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max_iter = 300; % Maximum iterations
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tol = 1e-4; % Tolerance
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% Methods tuning
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amijo_beta = 0.5; % Armijo reduction factor
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amijo_sigma = 0.1; % Armijo condition constant
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m = 0.01;
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% Point x0 = (0, 0)
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% x0 = [0, 0];
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% Point x0 = (0, 0)
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x0s = [0, 0; -1, 1 ; 1, -1]; % Initial points
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for i = 1:size(x0s, 1)
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x0 = x0s(i, :);
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point_str = "[" + x0(1) + ", " + x0(2) + "]";
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% Find the best fixed gamma
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k = zeros(100, 1);
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j = 1;
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n = linspace(0.1, 1.5, 100);
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for g = n
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gamma_fixed_step = g;
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[~, ~, k(j)] = lev_mar(fun, grad_fun, hessian_fun, m, x0, tol, max_iter, 'fixed');
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j = j + 1;
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end
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plotIterationsOverGamma(n, k, "Iteration for different $\gamma$ values", "LevMar_Iter_o_gamma_" + i + ".png");
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[~, j] = min(k);
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gamma_fixed_step = n(j);
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[x_fixed, f_fixed, kk] = lev_mar(fun, grad_fun, hessian_fun, m, x0, tol, max_iter, 'fixed');
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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));
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plotPointsOverContour(x_fixed, fun, [-2, 2], [-3, 3], 100, point_str + ": LevMar $\gamma$ = " + gamma_fixed_step, "LevMar_fixed_" + i + ".png");
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% Minimized f
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[x_minimized, f_minimized, kk] = lev_mar(fun, grad_fun, hessian_fun, m, x0, tol, max_iter, 'minimized');
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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));
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plotPointsOverContour(x_minimized, fun, [-2, 2], [-3, 3], 100, point_str + ": LevMar minimized $f(x_k + \gamma_kd_k)$", "LevMar_minimized_" + i + ".png");
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% Armijo Rule
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[x_armijo, f_armijo, kk] = lev_mar(fun, grad_fun, hessian_fun, m, x0, tol, max_iter, 'armijo');
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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));
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plotPointsOverContour(x_armijo, fun, [-2, 2], [-3, 3], 100, point_str + ": LevMar Armijo method", "LevMar_armijo_" + i + ".png");
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end
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