61 lines
2.0 KiB
Matlab
61 lines
2.0 KiB
Matlab
function [x_vals, f_vals, k] = method_lev_mar(f, grad_f, hessian_f, e, xk, 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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% hessian_f: Hessian of the function
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% e: Offset for hessian damping Hk' = Hk + mI
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% - when: Hk not positive defined
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% - Where: m = abs(min(eig(Hk))) + e
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% xk: Initial point [xk, yk]
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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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x_vals = xk; % Store iterations
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f_vals = f(xk(1), xk(2));
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for k = 1:max_iter
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grad = grad_f(xk(1), xk(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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hess = hessian_f(xk(1), xk(2));
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% Check if hessian is not positive defined
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lmin = min(eig(hess));
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if lmin <= 0
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% Select m with offset to stear hess to positive eigenvalues
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m = abs(lmin) + e;
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mI = m * eye(size(hess));
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if min(eig(hess + mI)) <= 0 % Fail-check
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warning('Can not normalize hessian matrix.');
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end
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end
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% Solve for search direction using Newton's step
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dk = - inv(hess + mI) * grad;
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% Calculate gamma
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gk = gamma_f(f, grad_f, dk, xk);
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x_next = xk + gk * dk'; % Update step
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f_next = f(x_next(1), x_next(2));
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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 |