eval_alx

 Evaluate Augmented Lagrangian at the current 'xall' point with the current
 penalty parameters and Lagrangian multipliers. The result will be stored
 in 'obj.ALx' and its ticker updated. All equalities 'obj.eqx' get updated
 as well. Return nonzero if evaluation failed (matrix not pos def, etc.) and 
 in this case, the value ALx will be set to Inf.

0001 % Evaluate Augmented Lagrangian at the current 'xall' point with the current
0002 % penalty parameters and Lagrangian multipliers. The result will be stored
0003 % in 'obj.ALx' and its ticker updated. All equalities 'obj.eqx' get updated
0004 % as well. Return nonzero if evaluation failed (matrix not pos def, etc.) and
0005 % in this case, the value ALx will be set to Inf.
0006 function [status] = eval_alx(obj)
0007   
0008   % TODO ... set status when cannot evaluate or something like that
0009   status=0;
0010 
0011   % work only if the value is out of date
0012   if (obj.ALxtck < obj.ticker)
0013     starttime = cputime;
0014     
0015     % create local copies of obj.x,obj.Y to avoid checking repetitively if they
0016     % are 'up-to-date' with obj.xall, they get used many times in calls to
0017     % user's functions
0018     x=obj.x;
0019     Y=obj.Y;
0020     % same for obj.userdata, it might be quite expensive to get&store it in
0021     % the object
0022     userdata=obj.userdata;
0023 
0024     [fx, userdata] = obj.objfun(x, Y, userdata);
0025     obj.objx=fx;
0026 
0027     % function inequal & equal
0028     %ineqx = zeros(obj.Nineq,1);   % probably not necessary, rather = []?
0029     ineqx=[];
0030     %obj.eqx = zeros(obj.Neq,1);
0031     if (obj.NgNLN + obj.NgLIN>0)
0032       [gx, userdata] = obj.confun(x, Y, userdata);
0033       ineqx = obj.ineqshift + obj.ineqmlt .* gx(obj.ineqmap);
0034       obj.ineqx = ineqx;
0035       obj.eqx = obj.eqshift + gx(obj.eqmap);
0036     end
0037     
0038     % box constraints
0039     xboxx = [];
0040     if (obj.Nxbox>0)
0041       xboxx = obj.xboxshift + obj.xboxmlt .* obj.xall(obj.xboxmap);
0042       obj.xboxx=xboxx;
0043     end
0044 
0045     ALx=fx;
0046 
0047     %  inequalitites: phi or bar?
0048     %  L = L + u'*(p.*phi2(g./p));
0049     %  L = L + u(i)*p(i)*phi2(g(i)/p(i));
0050 
0051     % box constraints
0052     ind=obj.xboxindbar;
0053     if (~isempty(ind))
0054       ALx=ALx + obj.uxbox(ind)'*(obj.pxbox(ind).*obj.phibar(xboxx(ind)));
0055     end
0056 
0057     ind=obj.xboxindphi;
0058     if (~isempty(ind))
0059       ALx=ALx + obj.uxbox(ind)'*(obj.pxbox(ind).*obj.phi2(xboxx(ind)./obj.pxbox(ind)));
0060     end
0061 
0062     % function inequalitites
0063     %ind=obj.ineqindbar;
0064     %if (~isempty(ind))
0065     %  ALx=ALx + obj.uineq(ind)'*(obj.pineq(ind).*phibar(ineqx(ind)));
0066     %end
0067 
0068     ind=obj.ineqindphi;
0069     if (~isempty(ind))
0070       ALx=ALx + obj.uineq(ind)'*(obj.pineq(ind).*obj.phi2(ineqx(ind)./obj.pineq(ind)));
0071     end
0072 
0073     % (function) equalities
0074     if (obj.Neq>0)
0075       ALx = ALx + obj.ueq'*obj.eqx;
0076     end
0077 
0078     % matrix variable - log barrier (strict feasibility)
0079     if ~isempty(obj.Yboxindbar)
0080     for k=obj.Yboxindbar
0081       % convert the matrix box constraint to the form:   +/-Y +/-bound >=0
0082       pkx=obj.PYbox(k);
0083       Ykx = Y{obj.Yboxmap(k)};
0084       Akx=-obj.Yboxshift(k)*speye(size(Ykx)) - obj.Yboxmlt(k)*Ykx;
0085       % check that it is pos. def.
0086       [R,iii]=chol(Akx);
0087       if (iii~=0)
0088         ALx=Inf;
0089         % jump out and even avoid anything other cycle
0090         break;  
0091       end
0092 
0093       % compute penalty term: -p*log(det(A)) = -p*log( det(R)^2 ) =
0094       %    = -2*p*log( prod(diag(R)) ) = -2*p*sum(log( diag(R) ))
0095       ALx = ALx -2*pkx*sum(log(diag(R)));
0096 
0097     end
0098     end
0099 
0100 
0101     % matrix variable - pen/bar
0102     if ~isempty(obj.Yboxindphi)
0103     for k=obj.Yboxindphi
0104       pkx=obj.PYbox(k);            %2*p(sdpdata.Ng+k);
0105       Ykx = Y{obj.Yboxmap(k)};
0106       Akx=obj.Yboxshift(k)*speye(size(Ykx)) + obj.Yboxmlt(k)*Ykx;
0107       umatk=obj.UYbox{k};
0108 
0109       %Z=(pkx*speye(size(Akx))-Akx);
0110       Z=(pkx*speye(size(Akx))-Akx);
0111       [R,iii]=chol(Z);   % to double check that it is pos. def!
0112       if (iii~=0)
0113         ALx=Inf;
0114         % jump out and even avoid anything other cycle
0115         break;  
0116       end
0117         
0118       invZ=inv(Z);
0119       % ... TODO ...
0120       ALx = ALx + trace(pkx^2*umatk*invZ-pkx*umatk);
0121     end
0122     end
0123 
0124     % matrix constraints - pen/bar
0125     if ~isempty(obj.Aindphi)
0126     for k=obj.Aindphi
0127       pkx=obj.PA(k);  % I used to use 2*         !!!!!!!!
0128       % TODO need to map the matrix first! - is it correct???
0129       kuser=obj.Amap(k);
0130       [Akuserx, userdata] = obj.mconfun(x, Y, kuser, userdata);
0131       Akx = obj.Ashift(k)*speye(size(Akuserx)) + obj.Amlt(k) .* Akuserx;
0132       umatk=obj.UA{k};
0133 
0134       %Z=(pkx*speye(size(Akx))-Akx);
0135       Z=(pkx*speye(size(Akx))-Akx);
0136       [R,iii]=chol(Z);   % to double check that it is pos. def!
0137       if (iii~=0)
0138         ALx=Inf;
0139         break;
0140       end
0141       invZ=inv(Z);
0142       % ... TODO ...
0143       %ALx = ALx + trace(pkx^2*umatk*invZ-pkx*umatk);
0144       ALx = ALx + pkx^2*(umatk(:)'*invZ(:))-pkx*trace(umatk);
0145     end
0146     end
0147 
0148     % store user's data back in the object if it got changed
0149     obj.userdata=userdata;
0150 
0151     % update ticker
0152     obj.ALx = ALx;
0153     obj.ALxtck = obj.ticker;
0154 
0155     % update stats
0156     obj.stats_ncall_alx = obj.stats_ncall_alx + 1;
0157     obj.stats_time_alx = obj.stats_time_alx + cputime - starttime;
0158   end
0159