bpdq_d_r_iter : Douglas-Rachford Iteration [xstar,relerr_save]=bpdq_d_r_iter(proxf1,proxf2,gamma,lambda,x0,varargin) Implements Douglas-Rachford Splitting to solve xstar = argmin_x [ f1(x) + f2(x) ] Inputs: proxf1, proxf2 - function handles computing prox(gamma*f1), prox(gamma*f2) i.e., proxf1(y,gamma) solves argmin_x [ (1/2) |y-x|^2 + gamma * f(x) ] gamma, lambda - Douglas-Rachford algorithm parameters x0 - starting point Selectable control parameters: dr_maxiter - maximum # of iterations dr_relerr_thresh - relative error threshold to terminate iteration dr_verbosity - 0 to supress output, 1 to output relative error at each iteration Outputs : xstar - returned solution relerr_save - record of relative error of iterates; relerr_save(n) = ||x_n-x_(n-1)||/||x_n|| This file is part of BPDQ Toolbox (Basis Pursuit DeQuantizer) Copyright (C) 2009, the BPDQ Team (see the file AUTHORS distributed with this library) (See the notice at the end of the file.)
0001 % bpdq_d_r_iter : Douglas-Rachford Iteration 0002 % 0003 % [xstar,relerr_save]=bpdq_d_r_iter(proxf1,proxf2,gamma,lambda,x0,varargin) 0004 % 0005 % Implements Douglas-Rachford Splitting to solve 0006 % xstar = argmin_x [ f1(x) + f2(x) ] 0007 % 0008 % Inputs: 0009 % proxf1, proxf2 - function handles computing prox(gamma*f1), prox(gamma*f2) 0010 % i.e., proxf1(y,gamma) solves argmin_x [ (1/2) |y-x|^2 + gamma * f(x) ] 0011 % gamma, lambda - Douglas-Rachford algorithm parameters 0012 % x0 - starting point 0013 % 0014 % Selectable control parameters: 0015 % dr_maxiter - maximum # of iterations 0016 % dr_relerr_thresh - relative error threshold to terminate iteration 0017 % dr_verbosity - 0 to supress output, 1 to output relative error at each 0018 % iteration 0019 % 0020 % Outputs : 0021 % xstar - returned solution 0022 % relerr_save - record of relative error of iterates; 0023 % relerr_save(n) = ||x_n-x_(n-1)||/||x_n|| 0024 % 0025 % This file is part of BPDQ Toolbox (Basis Pursuit DeQuantizer) 0026 % Copyright (C) 2009, the BPDQ Team (see the file AUTHORS distributed with 0027 % this library) (See the notice at the end of the file.) 0028 0029 function [xstar,relerr_save]=bpdq_d_r_iter(proxf1,proxf2,gamma,lambda,... 0030 x0,varargin) 0031 control_params={'dr_maxiter',500,... 0032 'dr_relerr_thresh',1e-6,... 0033 'dr_verbosity',0}; 0034 argselectAssign(control_params); 0035 argselectCheck(control_params,varargin); 0036 argselectAssign(varargin); 0037 0038 xp_old=zeros(size(x0)); 0039 xp_new=zeros(size(x0)); 0040 x_new=zeros(size(x0)); 0041 x_old=x0; 0042 for n=1:dr_maxiter 0043 xp_old=xp_new; 0044 if (n>1) 0045 x_old=x_new; 0046 end 0047 0048 xp_new=proxf1(x_old,gamma); 0049 x_new = x_old + lambda*(proxf2(2*xp_new-x_old,gamma)-xp_new); 0050 relerr = norm(xp_old-xp_new)/norm(xp_new); 0051 relerr_save(n)=relerr; 0052 if (dr_verbosity>=1) 0053 fprintf('DR iter %g, relerr = %g\n',n,relerr); 0054 end 0055 if (relerr<dr_relerr_thresh) && (n>3) 0056 break; 0057 end 0058 %keyboard 0059 end 0060 xstar=proxf1(x_new,gamma); 0061 0062 % The BPDQ Toolbox is free software: you can redistribute it and/or modify 0063 % it under the terms of the GNU General Public License as published by 0064 % the Free Software Foundation, either version 3 of the License, or 0065 % (at your option) any later version. 0066 % 0067 % The BPDQ Toolbox is distributed in the hope that it will be useful, 0068 % but WITHOUT ANY WARRANTY; without even the implied warranty of 0069 % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 0070 % GNU General Public License for more details. 0071 % 0072 % You should have received a copy of the GNU General Public License 0073 % along with The BPDQ Toolbox. If not, see <http://www.gnu.org/licenses/>.