45 lines
1.3 KiB
Matlab
45 lines
1.3 KiB
Matlab
function [x_vals, f_vals, k] = steepest_descent(f, grad_f, x0, tol, max_iter, mode)
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% f: Objective function
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% grad_f: Gradient of the function
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% x0: Initial point [x0, y0]
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% tol: Tolerance for stopping criterion
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% max_iter: Maximum number of iterations
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% x_vals: Vector with the (x,y) values until minimum
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% f_vals: Vector with f(x,y) values until minimum
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% k: Number of iterations
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if strcmp(mode, 'armijo') == 1
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gamma_f = @(f, grad_f, x0) gamma_armijo(f, grad_f, x0);
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elseif strcmp(mode, 'minimized') == 1
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gamma_f = @(f, grad_f, x0) gamma_minimized(f, grad_f, x0);
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else % mode == 'fixed'
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gamma_f = @(f, grad_f, x0) gamma_fixed(f, grad_f, x0);
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end
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% Storage for iterations, begin with the first point
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x_vals = x0;
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f_vals = f(x0(1), x0(2));
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for k = 1:max_iter
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grad = grad_f(x0(1), x0(2));
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% Check for convergence
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if norm(grad) < tol
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break;
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end
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dk = - grad;
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% Calculate gamma
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gk = gamma_f(f, grad_f, x0);
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x_next = x0 + gk * dk'; % Update step
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f_next = f(x_next(1), x_next(2));
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x0 = x_next; % Update point
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x_vals = [x_vals; x_next]; % Store values
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f_vals = [f_vals; f_next]; % Store function values
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end
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end
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