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matRad_projectedLBFGS.m
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matRad_projectedLBFGS.m
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function wOpt = matRad_projectedLBFGS(objFunc,projFunc,wInit,visBool,varargin)
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% projected L-BFGS optimizer including a positivity constraints on the
% optimization variable
%
% call
% optResult = matRad_projectedLBFGS(objFunc,wInit)
%
% input
% objFunc: objective function to be optimized
% wInit: start solution for optimizer
% visBool: plots the objective function value in dependence of the
% number of iterations
% varargin: optional: number of iterations and precision
%
% output
% wOpt: optimized vector
%
% References
% [1] Kelley: Iterative methods for optimization 1999
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% Copyright 2015, Mark Bangert, on behalf of the matRad development team
%
%
% This file is part of matRad.
%
% matrad is free software: you can redistribute it and/or modify it under
% the terms of the GNU General Public License as published by the Free
% Software Foundation, either version 3 of the License, or (at your option)
% any later version.
%
% matRad is distributed in the hope that it will be useful, but WITHOUT ANY
% WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
% FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
% details.
%
% You should have received a copy of the GNU General Public License in the
% file license.txt along with matRad. If not, see
% <http://www.gnu.org/licenses/>.
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% variables for termination criteria
iter = 0;
if isempty(varargin{1,1})
numOfIter = 1000;
prec = 1e-5;
else
optParam = varargin{1,1};
numOfIter = optParam{1,1}.numOfIter;
prec = optParam{1,1}.prec;
end
numOfParameters = numel(wInit);
% plot objective function output
if visBool
try
figHandles = get(0,'Children');
IdxHandle = [];
if ~isempty(figHandles)
v=version;
if str2num(v(1:3))>=8.5
IdxHandle = strcmp({figHandles(:).Name},'Progress of Optimization');
else
IdxHandle = strcmp(get(figHandles,'Name'),'Progress of Optimization');
end
end
if ~isempty(IdxHandle) && length(IdxHandle) > 1
figOpt = figHandles(IdxHandle);
AxesInfigOpt = findall(figOpt,'type','axes');
set(AxesInfigOpt,'NextPlot', 'replacechildren')
v=version;
if str2num(v(1:3))>=8.5
delete(AxesInfigOpt.Children);
else
children = get(AxesInfigOpt,'children');
delete(children);
end
else
figOpt=figure('Name','Progress of Optimization','NumberTitle','off');
hold on, grid on, grid minor,
AxesInfigOpt = findall(figOpt,'type','axes');
end
set(AxesInfigOpt,'YScale','log');
title(AxesInfigOpt,'Progress of Optimization','LineWidth',14),
xlabel(AxesInfigOpt,'# iterations','Fontsize',14),ylabel(AxesInfigOpt,'objective function value','Fontsize',14)
catch
warning('couldnt initialize figure to plot the objective value')
end
end
% initialize LBFGS optimizer
historyCounter = 0;
mem = 10; % number of past gradients and function values used for inverse hessian contruction
x = NaN*ones(numOfParameters,mem);
x(:,1) = wInit;
[~,isConstrActive] = projFunc(x(:,1));
objFuncValue = NaN*ones(1,mem);
dx = NaN*ones(numOfParameters,mem);
s_k = ones(numOfParameters,mem-1);
y_k = ones(numOfParameters,mem-1);
r_k = ones(mem-1,1);
a_k = ones(1,mem-1);
% 1st calculation of objective function and gradient
[objFuncValue(1),dx(:,1)] = objFunc(wInit);
objFuncValue(2:end) = 2*objFuncValue(1);
% convergence if change in objective function smaller than prec or maximum
% number of iteration reached. no convergence if lbfgs has just been rest
continueOpt = 1;
convergenceLag = 1;
while continueOpt == 1
% implementation of L-BFGS according to
% http://en.wikipedia.org/wiki/L-BFGS
% inverse hessian update
q = dx(:,1);
for i = 1:historyCounter
a_k(i) = r_k(i)*s_k(:,i)'*q;
q = q - a_k(i)*y_k(:,i);
end
z = s_k(:,1)'*y_k(:,1)/(y_k(:,1)'*y_k(:,1))*q; % this corresponds to H*q where H is approximated as described in Nocedal 9.1
for i = historyCounter:-1:1
b = r_k(i)*y_k(:,i)'*z;
z = z + s_k(:,i)*(a_k(i)-b);
end
% obtain search direction
dir = -z; % this is the lbfgs direction!
% 2.1 armijo linesearch to to find acceptable stepsize alpha
alpha = 10;
fac = 1/10; % < 1 reduction factor of alpha
c_1 = 1e-10;
continueLineSearch = true;
expectedDescend = (~isConstrActive.*dir)'*dx(:,1);
fprintf('Starting line search ')
while continueLineSearch
alpha = fac*alpha;
candidateX = x(:,1) + alpha*dir;
% project candidate to feasible set
[candidateX, isConstrActive] = projFunc(candidateX);
% evaluate objective function and gradient
[lineSearchObjFuncValue,lineSearchDx] = objFunc(candidateX);
% check if armijo criterion fulfilled
continueLineSearch = lineSearchObjFuncValue > objFuncValue(1) + c_1*alpha*expectedDescend;
if alpha < 1e-10;
%fprintf('Error in Line search - alpha close to working precision...\n');
fprintf(1,'Performed 10 line searches - Resetting LBFGS update\n');
s_k = ones(numOfParameters,mem-1);
y_k = ones(numOfParameters,mem-1);
r_k = ones(mem-1,1);
a_k = ones(1,mem-1);
historyCounter = 0;
break;
end
fprintf('.')
end
fprintf('\n')
% 2.2 update x
x(:,2:end) = x(:,1:end-1);
dx(:,2:end) = dx(:,1:end-1);
x(:,1) = candidateX;
objFuncValue(2) = objFuncValue(1);
objFuncValue(1) = lineSearchObjFuncValue;
dx(:,1) = lineSearchDx;
s_k = -diff(x,[],2);
y_k = -diff(dx,[],2);
s_k(isConstrActive,1) = 0;
y_k(isConstrActive,1) = 0;
r_k = 1./diag(y_k'*s_k);
% increment iteration counter
iter = iter + 1;
historyCounter = min(historyCounter+1,mem-1);
if (s_k(:,1)'*y_k(:,1)) <= 0
fprintf(1,'Resetting LBFGS update\n');
s_k = ones(numOfParameters,mem-1);
y_k = ones(numOfParameters,mem-1);
r_k = ones(mem-1,1);
a_k = ones(1,mem-1);
historyCounter = 0;
end
fprintf(1,'Iteration %d: alpha = %f, Obj func = %f\n',iter,alpha,objFuncValue(1));
continueOpt = (iter < numOfIter && abs((objFuncValue(1+convergenceLag)-objFuncValue(1))/objFuncValue(1))>prec) || historyCounter < 2 ;
if objFuncValue(2)== 0 && objFuncValue(1) == 0
continueOpt = 0;
disp('objective function reached theoretical minimum f = 0 - this is fishy. please double check your optimization objectives.')
end
if visBool
objFuncValues{iter}=objFuncValue(1);
axes(AxesInfigOpt)
plot(AxesInfigOpt,1:1:iter,cell2mat(objFuncValues),'b','Linewidth',3);
drawnow
end
end
fprintf(['\n' num2str(iter) ' iteration(s) performed to converge\n'])
wOpt = x(:,1);