updating lmmcp.m from RECS
Michel Juillard
parent
1d9aee20f2
commit
214610be1e
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@ -22,9 +22,10 @@ function [x,FVAL,EXITFLAG,OUTPUT,JACOB] = lmmcp(FUN,x,lb,ub,options,varargin)
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% preprocess : activate preprocessor for phase I (default = 1)
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% presteps : number of iterations in phase I (default = 20)
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% Termination parameters
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% epsilon2 : termination value of the merit function (default = 1E-16)
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% MaxIter : maximum number of iterations (default = 500)
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% MaxIter : Maximum number of iterations (default = 500)
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% tmin : safeguard stepsize (default = 1E-12)
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% TolFun : Termination tolerance on the function value, a positive
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% scalar (default = sqrt(eps))
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% Stepsize parameters
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% m : number of previous function values to use in the nonmonotone
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% line search rule (default = 10)
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@ -85,7 +86,7 @@ function [x,FVAL,EXITFLAG,OUTPUT,JACOB] = lmmcp(FUN,x,lb,ub,options,varargin)
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% e-mail: kanzow@mathematik.uni-wuerzburg.de
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% petra@mathematik.uni-wuerzburg.de
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% ------------Initialization----------------
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%% Initialization
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defaultopt = struct(...
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'beta', 0.55,...
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'Big', 1e10,...
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@ -93,7 +94,6 @@ defaultopt = struct(...
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'deltamin', 1,...
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'Display', 'none',...
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'epsilon1', 1e-6,...
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'epsilon2', 1e-16,...
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'eta', 0.95,...
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'kwatch', 20,...
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'lambda1', 0.1,...
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@ -106,6 +106,7 @@ defaultopt = struct(...
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'sigma1', 0.5,...
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'sigma2', 2,...
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'tmin', 1e-12,...
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'TolFun', sqrt(eps),...
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'watchdog', 1);
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if nargin < 4
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@ -122,21 +123,22 @@ else
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options = catstruct(defaultopt,options);
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end
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warning('off','MATLAB:rankDeficientMatrix')
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switch options.Display
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case {'off','none'}
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verbosity = 0;
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case {'iter','iter-detailed'}
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verbosity = 2;
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case {'final','final-detailed'}
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verbosity = 1;
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otherwise
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verbosity = 0;
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case {'off','none'}
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verbosity = 0;
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case {'iter','iter-detailed'}
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verbosity = 2;
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case {'final','final-detailed'}
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verbosity = 1;
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otherwise
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verbosity = 0;
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end
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% parameter settings
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eps1 = options.epsilon1;
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eps2 = options.epsilon2;
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eps2 = 0.5*options.TolFun^2;
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null = options.null;
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Big = options.Big;
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@ -212,14 +214,14 @@ aux(1) = Psix;
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MaxPsi = Psix;
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if watchdog==1
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kbest = k;
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xbest = x;
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Phibest = Phix;
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Psibest = Psix;
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DPhibest = DPhix;
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DPsibest = DPsix;
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normDPsibest = normDPsix;
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end;
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kbest = k;
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xbest = x;
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Phibest = Phix;
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Psibest = Psix;
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DPhibest = DPhix;
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DPsibest = DPsix;
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normDPsibest = normDPsix;
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end
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% initial output
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if verbosity > 1
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@ -229,76 +231,74 @@ if verbosity > 1
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fprintf('%4.0f %24.5e %24.5e\n',k,Psix,normDPsix);
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end
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%
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% Preprocessor using local method
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%
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%% Preprocessor using local method
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if preprocess==1
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if verbosity > 1
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disp('************************** Preprocessor ****************************')
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end
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normpLM=1;
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while (k < presteps) && (Psix > eps2) && (normpLM>null)
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k = k+1;
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% choice of Levenberg-Marquardt parameter, note that we do not use
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% the condition estimator for large-scale problems, although this
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% may cause numerical problems in some examples
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normpLM=1;
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while (k < presteps) && (Psix > eps2) && (normpLM>null)
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k=k+1;
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% choice of Levenberg-Marquardt parameter, note that we do not use
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% the condition estimator for large-scale problems, although this
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% may cause numerical problems in some examples
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i=0;
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mu=0;
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if n<100
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i=1;
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mu=1e-16;
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if condest(DPhix'*DPhix)>1e25
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mu=1e-6/(k+1);
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end
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i = false;
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mu = 0;
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if n<100
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i = true;
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mu = 1e-16;
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if condest(DPhix'*DPhix)>1e25
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mu = 1e-6/(k+1);
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end
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if i==1
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pLM= [ DPhix ; sqrt(mu)*speye(n)]\[-Phix;sparse(n,1)];
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else
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pLM=-DPhix\Phix;
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end
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normpLM=norm(pLM);
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end
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if i
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pLM = [DPhix; sqrt(mu)*speye(n)]\[-Phix; zeros(n,1)];
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else
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pLM = -DPhix\Phix;
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end
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normpLM = norm(pLM);
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% compute the projected Levenberg-Marquard step onto box Xk
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lbnew = max(min(lb-x,0),-delta);
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ubnew = min(max(ub-x,0),delta);
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d = max(lbnew,min(pLM,ubnew));
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xnew = x+d;
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% compute the projected Levenberg-Marquard step onto box Xk
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lbnew=max(min(lb-x,0),-delta);
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ubnew=min(max(ub-x,0),delta);
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d=max(lbnew,min(pLM,ubnew));
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xnew=x+d;
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% function evaluations etc.
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[Fxnew,DFxnew] = feval(FUN,xnew,varargin{:});
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Phixnew = Phi(xnew,Fxnew,lb,ub,lambda1,lambda2,n,Indexset);
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Psixnew = 0.5*(Phixnew'*Phixnew);
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normPhixnew = norm(Phixnew);
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% update of delta
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if normPhixnew<=eta*normPhix
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delta = max(deltamin,sigma2*delta);
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elseif normPhixnew>5*eta*normPhix
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delta = max(deltamin,sigma1*delta);
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end
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% function evaluations etc.
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[Fxnew,DFxnew] = feval(FUN,xnew,varargin{:});
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Phixnew=Phi(xnew,Fxnew,lb,ub,lambda1,lambda2,n,Indexset);
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Psixnew=0.5*(Phixnew'*Phixnew);
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normPhixnew=norm(Phixnew);
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% update of delta
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if normPhixnew<=eta*normPhix
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delta=max(deltamin,sigma2*delta);
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elseif normPhixnew>5*eta*normPhix
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delta=max(deltamin,sigma1*delta);
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end
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% update
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x=xnew;
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Fx=Fxnew;
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DFx=DFxnew;
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Phix=Phixnew;
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Psix=Psixnew;
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normPhix=normPhixnew;
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DPhix=DPhi(x,Fx,DFx,lb,ub,lambda1,lambda2,n,Indexset);
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DPsix=DPhix'*Phix;
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normDPsix=norm(DPsix,inf);
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% output at each iteration
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t=1;
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if verbosity > 1
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fprintf('%4.0f %24.5e %24.5e %11.7g\n',k,Psix,normDPsix,t);
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end
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end
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% update
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x = xnew;
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Fx = Fxnew;
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DFx = DFxnew;
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Phix = Phixnew;
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Psix = Psixnew;
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normPhix = normPhixnew;
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DPhix = DPhi(x,Fx,DFx,lb,ub,lambda1,lambda2,n,Indexset);
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DPsix = DPhix'*Phix;
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normDPsix = norm(DPsix,inf);
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% output at each iteration
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t=1;
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if verbosity > 1
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fprintf('%4.0f %24.5e %24.5e %11.7g\n',k,Psix,normDPsix,t);
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end
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end
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end
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% terminate program or redefine current iterate as original initial point
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@ -323,12 +323,10 @@ elseif preprocess==1 && Psix>=eps2
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if verbosity > 1
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disp('******************** Restart with initial point ********************')
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fprintf('%4.0f %24.5e %24.5e\n',k_main,Psix0,normDPsix0);
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end
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end
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end
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%
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% Main algorithm
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%
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%% Main algorithm
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if verbosity > 1
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disp('************************** Main program ****************************')
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@ -336,96 +334,96 @@ end
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while (k < kmax) && (Psix > eps2)
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% choice of Levenberg-Marquardt parameter, note that we do not use
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% the condition estimator for large-scale problems, although this
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% may cause numerical problems in some examples
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% choice of Levenberg-Marquardt parameter, note that we do not use
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% the condition estimator for large-scale problems, although this
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% may cause numerical problems in some examples
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i=0;
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if n<100
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i=1;
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mu=1e-16;
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if condest(DPhix'*DPhix)>1e25
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mu=1e-1/(k+1);
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end
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end
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i = false;
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if n<100
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i = true;
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mu = 1e-16;
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if condest(DPhix'*DPhix)>1e25
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mu = 1e-1/(k+1);
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end
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end
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% compute a Levenberg-Marquard direction
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% compute a Levenberg-Marquard direction
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if i
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d = [DPhix; sqrt(mu)*speye(n)]\[-Phix; zeros(n,1)];
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else
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d = -DPhix\Phix;
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end
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if i==1
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d= [ DPhix ; sqrt(mu)*eye(n)]\[-Phix;zeros(n,1)];
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else
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d=-DPhix\Phix;
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end
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% computation of steplength t using the nonmonotone Armijo-rule
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% starting with the 6-th iteration
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% computation of steplength t using the nonmonotone Armijo-rule
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% starting with the 6-th iteration
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% computation of steplength t using the monotone Armijo-rule if
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% d is a 'good' descent direction or k<=5
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% computation of steplength t using the monotone Armijo-rule if
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% d is a 'good' descent direction or k<=5
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t = 1;
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xnew = x+d;
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Fxnew = feval(FUN,xnew,varargin{:});
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Phixnew = Phi(xnew,Fxnew,lb,ub,lambda1,lambda2,n,Indexset);
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Psixnew = 0.5*(Phixnew'*Phixnew);
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const = sigma*DPsix'*d;
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while (Psixnew > MaxPsi + const*t) && (t > tmin)
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t = t*beta;
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xnew = x+t*d;
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Fxnew = feval(FUN,xnew,varargin{:});
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Phixnew = Phi(xnew,Fxnew,lb,ub,lambda1,lambda2,n,Indexset);
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Psixnew = 0.5*(Phixnew'*Phixnew);
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end
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t = 1;
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xnew = x+d;
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Fxnew = feval(FUN,xnew,varargin{:});
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Phixnew = Phi(xnew,Fxnew,lb,ub,lambda1,lambda2,n,Indexset);
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Psixnew = 0.5*(Phixnew'*Phixnew);
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const = sigma*DPsix'*d;
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while (Psixnew > MaxPsi + const*t) && (t > tmin)
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t = t*beta;
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xnew = x+t*d;
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Fxnew = feval(FUN,xnew,varargin{:});
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Phixnew = Phi(xnew,Fxnew,lb,ub,lambda1,lambda2,n,Indexset);
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Psixnew = 0.5*(Phixnew'*Phixnew);
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end
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% updatings
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x=xnew;
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Fx=Fxnew;
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Phix=Phixnew;
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Psix=Psixnew;
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[~,DFx]=feval(FUN,x,varargin{:});
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DPhix=DPhi(x,Fx,DFx,lb,ub,lambda1,lambda2,n,Indexset);
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DPsix=DPhix'*Phix;
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normDPsix=norm(DPsix);
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k=k+1;
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k_main=k_main+1;
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if k_main<=5
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aux(mod(k_main,m)+1)=Psix;
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% updatings
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x = xnew;
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Fx = Fxnew;
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Phix = Phixnew;
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Psix = Psixnew;
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[~,DFx] = feval(FUN,x,varargin{:});
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DPhix = DPhi(x,Fx,DFx,lb,ub,lambda1,lambda2,n,Indexset);
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DPsix = DPhix'*Phix;
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normDPsix = norm(DPsix);
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k = k+1;
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k_main = k_main+1;
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if k_main<=5
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aux(mod(k_main,m)+1) = Psix;
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MaxPsi = Psix;
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else
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aux(mod(k_main,m)+1) = Psix;
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MaxPsi = max(aux);
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end
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% updatings for the watchdog strategy
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if watchdog ==1
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if Psix<Psibest
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kbest = k;
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xbest = x;
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Phibest = Phix;
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Psibest = Psix;
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DPhibest = DPhix;
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DPsibest = DPsix;
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normDPsibest = normDPsix;
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elseif k-kbest>kwatch
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x=xbest;
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Phix=Phibest;
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Psix=Psibest;
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DPhix=DPhibest;
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DPsix=DPsibest;
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normDPsix=normDPsibest;
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MaxPsi=Psix;
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else
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aux(mod(k_main,m)+1) = Psix;
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MaxPsi = max(aux);
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end;
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end
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end
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% updatings for the watchdog strategy
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if watchdog ==1
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if Psix<Psibest
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kbest = k;
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xbest = x;
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Phibest = Phix;
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Psibest = Psix;
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DPhibest = DPhix;
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DPsibest = DPsix;
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normDPsibest = normDPsix;
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elseif k-kbest>kwatch
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x=xbest;
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Phix=Phibest;
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Psix=Psibest;
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DPhix=DPhibest;
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DPsix=DPsibest;
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normDPsix=normDPsibest;
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MaxPsi=Psix;
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end;
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end;
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if verbosity > 1
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% output at each iteration
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fprintf('%4.0f %24.5e %24.5e %11.7g\n',k,Psix,normDPsix,t);
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end
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end
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if verbosity > 1
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% output at each iteration
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fprintf('%4.0f %24.5e %24.5e %11.7g\n',k,Psix,normDPsix,t);
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end
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end;
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% final output
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%% Final output
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if Psix<=eps2
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EXITFLAG = 1;
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if verbosity > 0, disp('Approximate solution found.'); end
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@ -446,9 +444,10 @@ OUTPUT.Psix = Psix;
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OUTPUT.normDPsix = normDPsix;
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JACOB = DFx;
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% Subfunctions
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%% Subfunctions
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function y = Phi(x,Fx,lb,ub,lambda1,lambda2,n,Indexset)
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%% PHI
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y = zeros(2*n,1);
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phi_u = sqrt((ub-x).^2+Fx.^2)-ub+x+Fx;
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@ -472,7 +471,7 @@ y([LZ; I3]) = lambda2*(max(0,x(I3)-lb(I3)).*max(0,Fx(I3))+max(0,ub(I3)-x(I3)).*m
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function H = DPhi(x,Fx,DFx,lb,ub,lambda1,lambda2,n,Indexset)
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% DPHI evaluates an element of the C-subdifferential of operator Phi
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%% DPHI evaluates an element of the C-subdifferential of operator Phi
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null = 1e-8;
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beta_l = zeros(n,1);
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@ -521,14 +520,14 @@ Da(I1b) = (x(I1b)-lb(I1b))./denom1(I1b)-1;
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Db(I1b) = Fx(I1b)./denom1(I1b)-1;
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I1b = Indexset==1 & beta_l~=0;
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if any(I1b)
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Da(I1b) = z(I1b)./denom2(I1b)-1;
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Db(I1b) = (DFx(I1b,:)*z)./denom2(I1b)-1;
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Da(I1b) = z(I1b)./denom2(I1b)-1;
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Db(I1b) = (DFx(I1b,:)*z)./denom2(I1b)-1;
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end
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I1a = I(Indexset==1 & alpha_l==1);
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I1a = I(Indexset==1 & alpha_l==1);
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if any(I1a)
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H2(I1a,:) = repmat(x(I1a)-lb(I1a),1,n).*DFx(I1a,:)+sparse(1:length(I1a),I1a, ...
|
||||
Fx(I1a),length(I1a),n,length(I1a));
|
||||
H2(I1a,:) = bsxfun(@times,x(I1a)-lb(I1a),DFx(I1a,:))+...
|
||||
sparse(1:length(I1a),I1a,Fx(I1a),length(I1a),n,length(I1a));
|
||||
end
|
||||
|
||||
I2 = Indexset==2;
|
||||
|
|
@ -544,14 +543,14 @@ Da(I2b) = (ub(I2b)-x(I2b))./denom1(I2b)-1;
|
|||
Db(I2b) = -Fx(I2b)./denom1(I2b)-1;
|
||||
I2b = Indexset==2 & beta_u~=0;
|
||||
if any(I2b)
|
||||
Da(I2b) = -z(I2b)./denom2(I2b)-1;
|
||||
Db(I2b) = -(DFx(I2b,:)*z)./denom2(I2b)-1;
|
||||
Da(I2b) = -z(I2b)./denom2(I2b)-1;
|
||||
Db(I2b) = -(DFx(I2b,:)*z)./denom2(I2b)-1;
|
||||
end
|
||||
|
||||
I2a = I(Indexset==2 & alpha_u==1);
|
||||
I2a = I(Indexset==2 & alpha_u==1);
|
||||
if any(I2a)
|
||||
H2(I2a,:) = repmat(x(I2a)-ub(I2a),1,n).*DFx(I2a,:)+sparse(1:length(I2a),I2a, ...
|
||||
Fx(I2a),length(I2a),n,length(I2a));
|
||||
H2(I2a,:) = bsxfun(@times,x(I2a)-ub(I2a),DFx(I2a,:))+...
|
||||
sparse(1:length(I2a),I2a,Fx(I2a),length(I2a),n,length(I2a));
|
||||
end
|
||||
|
||||
I3 = Indexset==3;
|
||||
|
|
@ -593,23 +592,23 @@ end
|
|||
Da(I3) = ai(I3)+bi(I3).*ci(I3);
|
||||
Db(I3) = bi(I3).*di(I3);
|
||||
|
||||
I3a = I(Indexset==3 & alpha_l==1 & alpha_u==1);
|
||||
I3a = I(Indexset==3 & alpha_l==1 & alpha_u==1);
|
||||
if any(I3a)
|
||||
H2(I3a,:) = repmat(-lb(I3a)-ub(I3a)+2*x(I3a),1,n).*DFx(I3a,:)+...
|
||||
2*sparse(1:length(I3a),I3a,Fx(I3a),length(I3a),n,length(I3a));
|
||||
H2(I3a,:) = bsxfun(@times,-lb(I3a)-ub(I3a)+2*x(I3a),DFx(I3a,:))+...
|
||||
2*sparse(1:length(I3a),I3a,Fx(I3a),length(I3a),n,length(I3a));
|
||||
end
|
||||
I3a = I(Indexset==3 & alpha_l==1 & alpha_u~=1);
|
||||
I3a = I(Indexset==3 & alpha_l==1 & alpha_u~=1);
|
||||
if any(I3a)
|
||||
H2(I3a,:) = repmat(x(I3a)-lb(I3a),1,n).*DFx(I3a,:)+...
|
||||
sparse(1:length(I3a),I3a,Fx(I3a),length(I3a),n,length(I3a));
|
||||
H2(I3a,:) = bsxfun(@times,x(I3a)-lb(I3a),DFx(I3a,:))+...
|
||||
sparse(1:length(I3a),I3a,Fx(I3a),length(I3a),n,length(I3a));
|
||||
end
|
||||
I3a = I(Indexset==3 & alpha_l~=1 & alpha_u==1);
|
||||
I3a = I(Indexset==3 & alpha_l~=1 & alpha_u==1);
|
||||
if any(I3a)
|
||||
H2(I3a,:) = repmat(x(I3a)-ub(I3a),1,n).*DFx(I3a,:)+...
|
||||
sparse(1:length(I3a),I3a,Fx(I3a),length(I3a),n,length(I3a));
|
||||
H2(I3a,:) = bsxfun(@times,x(I3a)-ub(I3a),DFx(I3a,:))+...
|
||||
sparse(1:length(I3a),I3a,Fx(I3a),length(I3a),n,length(I3a));
|
||||
end
|
||||
|
||||
%H1 = sparse(1:n,1:n,Da,n,n,n)+Db(:,ones(n,1)).*DFx;
|
||||
H1 = bsxfun(@times,Db,DFx);
|
||||
H1 = spdiags(diag(H1)+Da,0,H1);
|
||||
H = [lambda1*H1; lambda2*H2];
|
||||
H1 = bsxfun(@times,Db,DFx);
|
||||
H1 = spdiags(diag(H1)+Da,0,H1);
|
||||
|
||||
H = [lambda1*H1; lambda2*H2];
|
||||
|
|
|
|||
Loading…
Reference in New Issue