50 lines
1.8 KiB
Matlab
50 lines
1.8 KiB
Matlab
function [x_vals, f_vals, k] = method_SteepDesc_Proj(f, grad_f, xk, sk, limmits, 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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% xk: Initial point [x0; y0]
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% sk: Step size (fixed positive scalar)
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% limits: Bounds of the feasible set for each dimension
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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, dk, xk) gamma_armijo(f, grad_f, dk, xk);
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elseif strcmp(mode, 'minimized') == 1
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gamma_f = @(f, grad_f, dk, xk) gamma_minimized(f, grad_f, dk, xk);
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else % mode == 'fixed'
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gamma_f = @(f, grad_f, dk, xk) gamma_fixed(f, grad_f, dk, xk);
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end
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% Project the first point if needed
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xk = ProjectionPoint(xk, limmits);
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% Storage for iterations, begin with the first point
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x_vals = xk;
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f_vals = f(xk);
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for k = 1:max_iter
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% Check for convergence
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if norm(grad_f(xk)) < tol
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break;
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end
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dk = - grad_f(xk); % Steepset descent direction
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% First calculate xk-bar and project it if nessesary
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xkbar = xk + sk * dk;
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xkbar = ProjectionPoint(xkbar, limmits);
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dk = (xkbar - xk); % Steepest descent projection direction
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gk = gamma_f(f, grad_f, dk, xk); % Calculate gamma
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x_next = xk + gk * dk; % Update step
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f_next = f(x_next);
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xk = 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 |