linesearch.m
a1d561fb9dddmaster

linesearch.m
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			function [unext, gamma_out, nfeval] = linesearch(ucur, proj, f_lagrangian, grad_cur, gamma_in, theta)

			% This function is a linesearch routine which calcualtes the next iterate
			% with best possible choice of step size depending on the following rule:
			% min f(u), subject to A(u) = b, u \in \mathcal{C}
			% Augmented Lagrangian:
			% L(u, beta, yc) = f(u) + (beta)/2*\|\|A(u)-b\|\|^2 + <yc, A(u) - b>
			%
			% INPUT: ucur: Current iterate
			% proj: Projection operator onto set C
			% f_lagrangian: Callable to calculate lagrangian function value
			% grad_cur : Current gradient array in the size of u
			% gamma_in: Initial value for starting linesearch routine
			% theta: Decrease factor for step size
			% OUTPUT: unext: Next iterate
			% gamma_out: Step size after linesearch
			% nfeval: Number of function evaluations
			%
			% Author: Mehmet Fatih Sahin
			% Date : 28.12.2018
			if gamma_in < 1e-10
			gamma_in = 1e-2;
			end

			ls_max = 20; % maximum number of linesearch steps
			gamma_ls = gamma_in;
			fl2 = 0; fl1 = 0;
			for k = 1:ls_max
			u_in = proj(ucur - gamma_ls*grad_cur);
			if 1% abs(f_lagrangian(u_in) - (f_lagrangian(ucur))) > 1e-15
			if (f_lagrangian(u_in) > (f_lagrangian(ucur) + trace((u_in - ucur)'*grad_cur) ...
			+ 1/(2gamma_ls)norm(u_in - ucur, 2)^2))
			if fl1 == 0
			fl2 = 1;
			gamma_ls = gamma_ls/theta;
			else
			gamma_out = gamma_ls/theta;
			nfeval = k;
			return;
			end
			else
			if k == 1 \|\| fl2 == 1
			fl1 = 1;
			end
			gamma_ls = gamma_ls*theta;
			unext = u_in;
			end
			else
			gamma_out = gamma_ls;
			unext = u_in;
			nfeval = k;
			return
			end
			end
			nfeval = k;
			unext = u_in;
			gamma_out = gamma_ls;
			end