Matlab's MultiStart runs fine, but GlobalSearch bugs out

I'm trying to run a global optimization in Matlab using the global optimization toolbox. I am using the fmincon local optimizer as an input. I am able to successfully run the fmincon local optimizer, as well as the MultiStart global optimizer with this problem. However, when I try to set it up as a GlobalSearch, I get an error message.

Below is the code I am trying to use for the GlobalSearch:

%the functions is f(w) rather than f(x)

%constraints:
A = [1,0,0; 0,1,0; 0,0,1];
b = [.80, .80, .80];
Aeq = [1 1 1];
beq = 1;
lb = .10 * [1 1 1];
ub = .8 * [1 1 1];

w = [weight1, weight2, weight3];     
wstart = randn(3,1);

options = optimset('Algorithm','interior-point');

% function handle for the objective function (note that variables 
% aa through hh are additional parameters that the solver does not modify): 
h = @(w)Difference_in_Returns(w(1),w(2),w(3), aa, bb, cc, dd, ee, ff, gg, hh);

% problem structure:
problem = createOptimProblem('fmincon','x0',wstart,'objective',h,'Aineq',A,...'
'bineq',b,'Aeq',Aeq,'beq',beq,'options',options,'lb',lb,'ub',ub);

gs = GlobalSearch;
run(gs,problem)

When I try to run this, Matlab bugs out and prints:

Error using  - 
Matrix dimensions must agree.
Error in C:\Program Files\MATLAB\R2012a\toolbox\globaloptim\globaloptim\private\
globalsearchnlp.p>i_calcConstrViolation (line 593)

Error in C:\Program Files\MATLAB\R2012a\toolbox\globaloptim\globaloptim\private\
globalsearchnlp.p>i_calcPenalty (line 627)

Error in C:\Program Files\MATLAB\R2012a\toolbox\globaloptim\globaloptim\private\
globalsearchnlp.p>globalsearchnlp (line 343)

Error in GlobalSearch/run (line 330)
        [x,fval,exitflag,output] = ...
Error in Optimization_Setup (line 62)
run(gs,problem)

I believe the problem is outlined by the lines:

Error using  - 
Matrix dimensions must agree.
Error in GlobalSearch/run (line 330)
        [x,fval,exitflag,output] = ...

Any tips are highly appreciated. Please let me know if you have any questions.

Answer 1

[Shashank Prasanna]

Can you confirm that the objective function: h does not return Inf or NaN during its evaluations for all w?

Also in MultiStart how many runs are you specifying?

>> [x,f] = run(ms,problem,k)

Does it fail if you make k large?

[Anthony]

Thank you for your response.

Is there a way to verify whether an Inf or NaN for the objective function is the source of the problem (in other words: could I find out what value for w GlobalSearch is trying to use right before the error)? I would be very surprised if the function returned either of those values though...

I run MultiStart with 500 randomly generated start points. This takes about 4 minutes to run. How large should I be trying?

[Shashank Prasanna]

You must know if the objective function has a possibility of returning an inf or a nan. If not you can always check of the output using isinf and isnan functions.

In order to obtain intermediate values you can use outputfcn:

http://www.mathworks.com/help/gads/output-functions-for-globalsearch-and-multistart.html

The only reason I mentioned that you use a large enough start points is to verify if MultiStart would fail if it stepped on that special case that is making globalsearch fail.

One last point:

You have redundant constraints:

A = [1,0,0; 0,1,0; 0,0,1];
b = [.80, .80, .80];

is basically: x_i < 0.8 for i = 1,2,3

lb = .10 * [1 1 1];
ub = .8 * [1 1 1];

is basically: 0.1 < x_i < 0.8 for i = 1,2,3

Just use the bound constraints. Don't use both.