In a simultaneous fit (lsqcurvefit) with shared parameters how to supply the gradients for more than one objective functions

Hello everyone I realy need your help!!!

I am not able to supply the gradients analytically while curve fitting both real and imaginary data (lsqcurvefit). To be more specific I have several real and imaginary data sets with 5 shared parameters but with different objective functions, for example (Xdata1,Ydata1,objfun1),(Xdata2,Ydata2,objfun2),(Xdata3,Ydata3,objfun3) etc. I have created columns for the Xdata and Ydata and an array of anonymous objective functions for the various datasets. Finally i call the optimzation with multistart in parallel after I have created the problem. Now when the gradients are approximated by Finite Differences everything works very well but when I use the array of anonymous objective functions (more than 2) I am not able to supply the gradients analytically. The supplied gradients work only for a single objective function.

Is any workaround for this? Thanks in advance.

PS I tried a simpler example where fun3 is the objective function, m is a 4 parameter vector .

• fun= @(m,xdata)[fun3(m,xdata(1:20,1));fun3(m,xdata(21:end,1))];

• options = optimoptions('lsqcurvefit','Algorithm','trust-region-reflective',... 'OptimalityTolerance',1e-6,'MaxFunctionEvaluations',5e3, 'MaxIterations',5e3,'display','off',... 'TolFun',1e-6,'TolX',1e-6,'SpecifyObjectiveGradient',true);

• problem = createOptimProblem('lsqcurvefit','x0',m0start,'objective',fun,... 'lb',lb,'ub',ub,'xdata',xdata,'ydata',ydata,'options',options);

• ms = MultiStart('StartPointsToRun','all','UseParallel',true,'Display','off');

• [mbest,errorbest,exitflag,Fcount,soln] = run(ms,problem,tpoints);

and the output error is:

Error using vertcat

Too many output arguments.

Error in

@(m,xdata)[fun3(m,xdata(1:20,1));fun3(m,xdata(21:end,1))]

Error in lsqcurvefit (line 213)

[initVals.F,initVals.J] =

feval(funfcn_x_xdata{3},xCurrent,XDATA,varargin{:});

Error in fmultistart

Error in MultiStart/run (line 268)

fmultistart(problem,startPointSets,msoptions);

Caused by:

Failure in initial objective function evaluation. LSQCURVEFIT cannot continue.

Failure in call to the local solver with supplied problem structure.