Problem with matlabFunction and Nonlinear Optimization

I have been trying for a week to solve a problem I'm having using "matlabFunction" to convert a symbolic function to an anonymous function. The problem is that if I let "matlabFunction" run with the default settings it never finishes (I left it for 5 days before doing a control+c). If I turn off the default optimizer (i.e. 'Optimize',false) then matlabFunction returns a function different to that given by the original symbolic function and worse yet every point you evaluate the matlabFunction at returns a NaN whereas the symbolic function returns the proper value. Unfortunately the code I am working on is proprietary and I cannot post it. I have instead posted a sample function which uses the exact syntax I am using. The only difference in the code posted and the one I'm using is in "Jfunc(r)" where the posted one is just a generic polynomial.

clear all, close all, clc
r = sym('r',[1,9]);
assume(r,'real')
Jfunc(r) =  r(1)^2 + r(2)^3 + r(3)^4 + r(4)^5 + r(5)^6 + r(6)^7 + r(7)^8 + r(8)^9 + r(9)^10
Jfunc2 = matlabFunction(Jfunc,'Optimize',false)
JfuncFunc = @(r) Jfunc2(r(1),r(2),r(3),r(4),r(5),r(6),r(7),r(8),r(9))

lb = [0,0,0,0,0,0,0,0,0]; % Lowerbound of algebraic bounds on variables
ub = [1,1,1,1,1,1,1,1,1]; % Upperbound of algebraic bounds on variables
r0 = ones(1,9); %Initial parameters nondimensionalized [rho1,rho2,rho2,EI1,EI2,EI3,cA,cB,cC]
problem = createOptimProblem('fmincon','x0',r0,...
    'objective',JfuncFunc,'lb',lb,'ub',ub);

%Parallel Processing Multistart
ms = MultiStart('StartPointsToRun','bounds','UseParallel',true);
tic
parpool('IdleTimeout', 240)
[delta_updated,f] = run(ms,problem,100)
delete(gcp)
toc

The actual Junc(r) I am using is too long to post, it won't even display in the MATLAB window. However if I evaluate:

     Jfunc(1,1,1,1,1,1,1,1,1) = 0.000546
    Jfunc2(1,1,1,1,1,1,1,1,1) = NaN
  JfuncFunc([1,1,1,1,1,1,1,1,1]) = NaN

The code I posted runs fine however when I substitute in my more complicated function I get the following error:

Error using barrier
Objective function is undefined at initial point. Fmincon cannot continue.

Error in fmincon (line 798)
    [X,FVAL,EXITFLAG,OUTPUT,LAMBDA,GRAD,HESSIAN] = barrier(funfcn,X,A,B,Aeq,Beq,l,u,confcn,options.HessFcn, ...

Error in fmultistart

Error in MultiStart/run (line 271)
               fmultistart(problem,startPointSets,msoptions);

Error in CostFunctionOptimization_3BeamElms_test (line 238)
[delta_updated,f] = run(ms,problem,5000)

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

If I instead try to optimize Jfunc (a symfun) instead of JfuncFunc I get the following error (since the function returns sym and not double):

Error using fmincon (line 684)
FMINCON requires all values returned by functions to be of data type double.

Error in fmultistart

Error in MultiStart/run (line 271)
               fmultistart(problem,startPointSets,msoptions);

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

Does anyone have any suggestion on how I can perform this optimization either using a symfun or convert a symfun to anonymous without matlabFunction? Any help or suggestions would be greatly appreciated.

Answer 1

[Star Strider]

I’m not certain of the problem you’re experiencing. This works for me, and with the 'vars' name-value pair, produces a function with the appropriate syntax for the Optimization Toolbox and other functions:

r = sym('r',[1,9]);
assume(r,'real')
Jfunc(r) =  r(1)^2 + r(2)^3 + r(3)^4 + r(4)^5 + r(5)^6 + r(6)^7 + r(7)^8 + r(8)^9 + r(9)^10
Jfunc2 = matlabFunction(Jfunc, 'vars', [{r}])

Jfunc2 =

    function_handle with value:

      @(in1)in1(:,1).^2+in1(:,2).^3+in1(:,3).^4+in1(:,4).^5+in1(:,5).^6+in1(:,6).^7+in1(:,7).^8+in1(:,8).^9+in1(:,9).^10

This took a couple seconds, including the Command Window output (I didn’t time it).

[Ben]

Thank you for your comments and taking the time to look at my question. My problem is that the posted code works properly but when I replace the simple polynomial function "Jfunc" with my actual function matlabFunction either goes into a seemingly infinite loop trying to optimize the function or returns the incorrect function when I disable the optimizer. I'm trying to find a way to convert a symbolic function into a function which returns doubles without matlabFunction. I have attached a revised code below which will illustrate my problem using a condensed version of my actual function. Warning, it takes 10-15 minutes to run on my computer (which is why I posted the simple polynomial earlier, sounds like that was more confusing so I apologize). You will need to download the three .mat files and place them in the active directory for the code to run.

clear all, close all, clc
tic
r = sym('r',[1,9]);
assume(r,'real')

SRR = load('SRR.mat');
SRR = SRR.SRR;
Wi_Stacked = load('Wi_Stacked.mat');
Wi_Stacked = Wi_Stacked.Wi_Stacked;
SxxTilda_Stacked = load('SxxTilda_Stacked.mat');
SxxTilda_Stacked = SxxTilda_Stacked.SxxTilda_Stacked;

Jfunc(r) =  transpose(Wi_Stacked - SxxTilda_Stacked)*inv(SRR)*(Wi_Stacked - SxxTilda_Stacked);
Jfunc2 = matlabFunction(Jfunc,'Optimize',false);
JfuncFunc = @(r) Jfunc2(r(1),r(2),r(3),r(4),r(5),r(6),r(7),r(8),r(9));
lb = [0,0,0,0,0,0,0,0,0]; % Lowerbound of algebraic bounds on variables
ub = [1,1,1,1,1,1,1,1,1]; % Upperbound of algebraic bounds on variables
r0 = ones(1,9); %Initial parameters nondimensionalized [rho1,rho2,rho2,EI1,EI2,EI3,cA,cB,cC]
toc
problem = createOptimProblem('fmincon','x0',r0,...
    'objective',JfuncFunc,'lb',lb,'ub',ub);
%Parallel Processing Multistart
ms = MultiStart('StartPointsToRun','bounds','UseParallel',true);
tic
parpool('IdleTimeout', 240)
[delta_updated,f] = run(ms,problem,100)
delete(gcp)