unconstr_min

 unconstrained minimization
 returns in rResults=[aug_lagr(xBest),norm(grad(xBest)), norm(grad(x_0))]

 obj() etc. should work with one parameter x and return first parameter value/grad/hess
 expects an open nl-file?, N, N_EQUAL, ... global variables

 in the structure called 'fnc' there should be obj, obj_grad, obj_hess - functions to evaluate
 the equality constrainted problem

0001 function [nFlag,rResults]=unconstr_min(obj)
0002 % unconstrained minimization
0003 % returns in rResults=[aug_lagr(xBest),norm(grad(xBest)), norm(grad(x_0))]
0004 %
0005 % obj() etc. should work with one parameter x and return first parameter value/grad/hess
0006 % expects an open nl-file?, N, N_EQUAL, ... global variables
0007 %
0008 % in the structure called 'fnc' there should be obj, obj_grad, obj_hess - functions to evaluate
0009 % the equality constrainted problem
0010 
0011 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
0012 
0013   starttime=cputime;
0014   % reset default parameters if necessary
0015   MAX_MITER = obj.allopts.max_inner_iter;
0016   ALPHA = obj.allopts.inner_stop_limit;
0017   TOL_DIR = obj.allopts.unc_dir_stop_limit;
0018   solver = obj.allopts.unc_solver;
0019   linesearch = obj.allopts.unc_linesearch;
0020 
0021   miter=0;
0022 
0023   % x0 = xall as a starting point
0024   %fx=fnc.obj(x);
0025   %gradx=fnc.obj_grad(x);
0026   obj.eval_alx();
0027   obj.eval_aldx();
0028   fx_start = obj.ALx;
0029   rNormG = norm(obj.ALdx);
0030   rNormG_start = rNormG;
0031 
0032   obj.print(3,Inf,'object(x_%3i) = %24.16E',miter,obj.ALx);
0033   obj.print(3,Inf,'||grad(x)||_2 = %24.16E',rNormG);
0034   obj.print(4,Inf,'        --- start of inner iter ---');
0035   obj.print(4,Inf,' ');
0036   obj.print(3,4,'     ----');
0037 
0038   nFlag=1; % max it limit reached
0039   rResults=[];
0040   obj.initer_last=0;
0041   obj.lsiter_last=0;
0042   obj.stats_time_fact_last=0;
0043 
0044     while (miter < MAX_MITER)
0045 
0046       %hessx=fnc.obj_hess(x);
0047       obj.eval_alddx();
0048 
0049       %%%%%%%% Newton solver %%%%%%%%%
0050       switch solver
0051       case 0  % (Modified) Cholesky factorization
0052     [dir,nFlagSol] = obj.solve_chol(obj.ALddx,-obj.ALdx);
0053       %case 1  % CG+??
0054       %case   %
0055       %case   %
0056       otherwise
0057         obj.print(1,Inf,'unconstr_min() error: Sorry, no such solver, terminating...');
0058     nFlag=100;
0059     break;
0060       end
0061 
0062       if (nFlagSol>0)
0063         nFlag=2; % solver failed, cannot continue
0064     obj.print(3,Inf,'FAILURE: Newton solver (%i) cannot continue (flag %i)',solver,nFlagSol);
0065         break;
0066       end
0067 
0068       %%%%%%%% linesearch %%%%%%%%%
0069       switch linesearch
0070       case 0  % Do nothing, leave original data
0071      % such as x, grad_x (useful for TR, ...)
0072         nFlagLS = 0;
0073       case 1  % Do full steps, no linesearch at all
0074         [rRelStep, nFlagLS] = obj.ls_fullstep(dir);
0075       case 2  % Armijo linesearch
0076         [rRelStep, nFlagLS] = obj.ls_armijo(dir);
0077       case 3  % Pennlp/Pennon ("els) linesearch
0078         [rRelStep, nFlagLS] = obj.ls_pennon(dir);
0079       %case   %
0080       otherwise
0081         obj.print(1,Inf,'unconstr_min() error: Sorry, no such LS, terminating...');
0082     nFlag=100;
0083     break;
0084       end
0085 
0086       if (nFlagLS>0)
0087         nFlag=3; % LS failed, cannot continue
0088     obj.print(3,Inf,'FAILURE: Linesearch (%i) cannot continue (flag %i)',linesearch,nFlagLS);
0089         break;
0090       end
0091 
0092       %%%%%%%% %%%%%%%%%
0093       rNormG = norm(obj.ALdx);
0094       miter=miter+1;
0095 
0096       obj.print(4,Inf,' ');
0097       obj.print(3,Inf,'object(x_%3i) = %24.16E',miter,obj.ALx);
0098       obj.print(3,Inf,'||grad(x)||_2 = %24.16E',rNormG);
0099       obj.print(4,Inf,'        --- end of %3i in. iter ---\n',miter);
0100       obj.print(3,4,'     ----');
0101 
0102       %%%%%%%% stopping criterion %%%%%%%%%
0103       % just make it simple at the begining
0104       if (rNormG < ALPHA)
0105         nFlag=0;
0106     break;
0107       end
0108 
0109     end % of while
0110 
0111   if (nFlag==1)
0112     obj.print(3,Inf,'FAILURE: Unconstr minimization max iter (%i) reached.',miter);
0113   elseif (nFlag==0)
0114     obj.print(4,Inf,'Unconstr min OK');
0115   end
0116 
0117   rResults=[obj.ALx,rNormG, rNormG_start];
0118 
0119   % update stats
0120   obj.initer = obj.initer+obj.initer_last;
0121   obj.lsiter = obj.lsiter+obj.lsiter_last;
0122   obj.miter=obj.miter+miter;
0123   obj.miter_last=miter;
0124   obj.stats_time_miter_last = cputime - starttime;
0125   obj.stats_time_miters = obj.stats_time_miters + obj.stats_time_miter_last;
0126   obj.stats_time_fact = obj.stats_time_fact + obj.stats_time_fact_last;
0127 
0128   return;
0129