function [x,fval,stat] = gmnp(H,f,options)% GMNP Solves Generalized Minimal Norm Problem. %% Synopsis:%  [x,fval,stat] = gmnp(H,f)%  [x,fval,stat] = gmnp(H,f,options)%% Description:%  The Generalized Minimal Norm Problem to solve reads %%   argmin 0.5*x'*H*x + f'*x  subject to: sum(x) = 1 and x >= 0.%     x%%  H is symetric positive-definite matrix. The GMNP is a special%  instance of the Quadratig Programming (QP) task. The GMNP%  is solved by one of the following algorithms:%    mdm  ... Mitchell-Demyanov-Malozemov%    imdm  ... Improved Mitchell-Demyanov-Malozemov (default).%    iimdm  ... Improved (version 2) Mitchell-Demyanov-Malozemov.%    kozinec ... Kozinec algorithm.%    keerthi ... Derived from NPA algorithm by Keerthi et al.%    kowalczyk ... Based on Kowalczyk's maximal margin perceptron.%%  The optimization halts if one of the following stopping %  conditions is satisfied:%%    options.tolabs >= UB-LB          -> exitflag = 1%    options.tolrel*abs(UB) >= UB-LB  -> exitflag = 2%    options.thlb < LB                -> exitflag = 3%    options.tmax <= t                -> exitflag = 0% %  where t is number of iterations, UB and LB are upper and %  lower bounds on the optimal solution.%%  For more info refer to V.Franc: Optimization Algorithms for Kernel %  Methods. Research report. CTU-CMP-2005-22. CTU FEL Prague. 2005.%  ftp://cmp.felk.cvut.cz/pub/cmp/articles/franc/Franc-PhD.pdf .%% Input:%  H [dim x dim] Symetric positiove definite matrix.%  f [dim x 1] Vector.%  options [struct] Control parameters:%   .solver [string] Solver to be used: 'mdm', 'imdm' (default), 'iimdm', %     'kozinec', 'kowalczyk','keerthi'.%   .tmax [1x1] Maximal number of iterations (default inf).%   .tolabs [1x1] Absolute tolerance stopping condition (default 0.0).%   .tolrel [1x1] Relative tolerance stopping condition (default 0.001).%   .thlb [1x1] Thereshold on the lower bound (default inf).%   .verb [1x1] If > 0 then displays info every verb-th iteration (default 0).%% Output:%  x [dim x 1] Solution vector.%  fval [1x1] Value of the criterion at x.%  stat [struct] Constains:%   .exiflag [1x1] Exitflag (see above).%   .t [1x1] Number of iterations.%   .LB_History [1 x t] History of lower bounds.%   .UB_History [1 x t] History of upper bounds.%   .access [1x1] Number of accesses to the matrix H.%   .LB [1x1] == LB_History(end).%   .UB [1x1] == UB_History(end).%   .cputime [1x1] CPU time meassured by tic toc functions.%% Example:%  X = rand(50,200); f = rand(200,1); e = ones(200,1);%  tic; [x1,fval1] = gmnp(X'*X,f); toc, fval1%  tic; [x2,fval2] = quadprog(X'*X,f,[],[],e',1,e*0); toc, fval2%% See also %  GNNLS, RSDE, BSVM2.%% About: Statistical Pattern Recognition Toolbox% (C) 1999-2005, Written by Vojtech Franc and Vaclav Hlavac% <a href="http://www.cvut.cz">Czech Technical University Prague</a>% <a href="http://www.feld.cvut.cz">Faculty of Electrical Engineering</a>% <a href="http://cmp.felk.cvut.cz">Center for Machine Perception</a>% Modifications:% 09-sep-2005, VF% 24-jan-2005, VF% 20-nov-2004, VF% 16-jul-2004, VF% 29-jun-2004, VF% cputimertic;% optionsif nargin < 3, options = []; else options = c2s(options); endif ~isfield(options,'tolabs'), options.tolabs = 0; endif ~isfield(options,'tolrel'), options.tolrel = 1e-3; endif ~isfield(options,'thlb'), options.thlb = inf; endif ~isfield(options,'tmax'), options.tmax = inf; endif ~isfield(options,'verb'), options.verb = 0; endif ~isfield(options,'solver'), options.solver = 'imdm'; end[x,exitflag,t,access,History] = gmnp_mex( H, f, ...   options.solver,options.tmax,options.tolabs,options.tolrel,...   options.thlb, options.verb );stat.t = t;stat.exitflag = exitflag;stat.LB_History = History(1,:);stat.UB_History = History(2,:);stat.LB = History(1,end);stat.UB = History(2,end);stat.access = access;stat.cputime = toc;fval = stat.UB;return;% EOF