58 lines
1.4 KiB
Matlab
58 lines
1.4 KiB
Matlab
function [a, b, k, n] = min_bisection(fun_expr, alpha, beta, epsilon, lambda)
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% Bisection method for finding the local minimum of a function.
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%
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% fun_expr: (symbolic expression over x) The symbolic expression of the
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% objective function
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% alpha: (number) The starting point of the interval in which we seek
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% for minimum
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% beta: (number) The ending point of the interval in which we seek
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% for minimum
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% epsilon: (number) The epsilon value (distance from midpoint)
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% lambda: (number) The lambda value (accuracy)
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%
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% return:
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% a: (vector) Starting points of the interval for each iteration
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% b: (vector) Ending points of the interval for each iteration
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% k: (number) The number of iterations
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% n: (number) The calls of objective function fun_expr
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%
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% Error checking
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if alpha > beta || 2*epsilon >= lambda || lambda <= 0
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error ('Input criteria not met')
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end
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% Init
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a = alpha;
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b = beta;
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n = 0;
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fun = matlabFunction(fun_expr);
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% wrapper call count function
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function r = count_fun(x)
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n = n + 1;
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r = fun(x);
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end
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k=1;
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while b(k) - a(k) > lambda
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% bisect [a,b]
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mid = (a(k) + b(k)) / 2;
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x_1 = mid - epsilon;
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x_2 = mid + epsilon;
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% set new search interval
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k = k + 1;
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if count_fun(x_1) < count_fun(x_2)
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a(k) = a(k-1);
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b(k) = x_2;
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else
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a(k) = x_1;
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b(k) = b(k-1);
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end
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end
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end
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