39 lines
921 B
Matlab
39 lines
921 B
Matlab
function [xk, xs, gs] = BGFS(f, x0, H, max_itr, tol)
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syms x y;
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xk = x0;
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gf = gradient(f);
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fl = matlabFunction(f);
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gfl = matlabFunction(gf);
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tnorm = norm(at(gf, xk), 2);
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xs = zeros(size(x0, 1), max_itr + 1);
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xs(:, 1) = x0;
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gs = zeros(1, max_itr + 1);
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gs(1) = tnorm;
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k = 1;
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I = eye(2);
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while tnorm > tol && k <= max_itr
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grad = gfl(xk(1), xk(2));
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p = -H * grad;
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alpha = backtracking(fl, gfl, p, xk, 1, 0.9, 1e-4);
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xk = xk + alpha * p;
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s = alpha * p;
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y = gfl(xk(1), xk(2)) - grad;
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rho = 1 / (y' * s);
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H = (I - (rho * s * y')) * H * (I - (rho * y * s')) ...
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+ (1 / (y' * s) * (s * s'));
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k = k + 1;
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xs(:, k) = xk;
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tnorm = norm(gfl(xk(1), xk(2)), 2);
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gs(k) = tnorm;
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end
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xs = xs(:, 1:k);
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gs = gs(:, 1:k);
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end |