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- % Define environment (functions, gradients etc...)
- GivenEnv
-
- % Define parameters
- max_iter = 300; % Maximum iterations
- tol = 1e-4; % Tolerance
-
- % Methods tuning
- amijo_beta = 0.5; % Armijo reduction factor
- amijo_sigma = 0.1; % Armijo condition constant
-
- % 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\n', x0, f, gf, hf);
-
- % Points x0 = (-1, 1), (1, -1)
- %x0s = [-1, 1 ; 1, -1]; % Initial points
-
- % 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, 2], [-2, 2], 100, point_str + ": Steepest descent minimized $f(x_k + \gamma_kd_k)$", "StDes_minimized_" + i + ".png");
-
-
- % Armijo Rule
- [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, 2], [-2, 2], 100, point_str + ": Steepest descent Armijo method", "StDes_armijo_" + i + ".png");
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