Failure of do loop after first step when applying globalsearch to a nonlinear least squares problem

Dear All,

I am trying to generate bootstrap standard errors for a nonlinear least-squares optimization.

The optimization works for the first run, but my do loop for generating repeated runs of the optimization stops after the first run.

I am using global search from the Global Optimization toolbox.

The error message is:

Index in position 1 exceeds array bounds (must not exceed 1).

Looking for help to solve this do loop problem.

Details are below.

Best,

Srinivasan

    My dependent variable y is an 18,026 by 1 vector
    My independent variable matrix X is 18,026 rows by 14 columns

    My parameter vector is x2 and is an 1 by 15 vector.

    I use globalsearch and nonlinear squares on the following function to generate an estimate of x2:

    function F2 = myfun2(x2,y,X)
    F2 = sum((((y - (1 + x2(1)*(x2(2)/0.0025662))*X(:,1) - (x2(2)/x2(3))*(sqrt(1-x2(1)^2))*X(:,2) - x2(4)*X(:,3) - x2(5)*X(:,4) - x2(6)*X(:,5) - x2(7)*X(:,6) - x2(8)*X(:,7) - x2(9)*X(:,8) - x2(10)*X(:,9) - x2(11)*X(:,10) - x2(12)*X(:,11) - x2(13)*X(:,12) - x2(14)*X(:,13) - x2(15)*X(:,14)))).^2);
    end

    gsproblem = createOptimProblem('fmincon','objective',@(x2) myfun2(x2, y, X),'x0',x0,'lb',lb,'ub',ub);

    gs = GlobalSearch('Display','iter');

    gs = GlobalSearch(gs,'XTolerance',1e-3,'StartPointsToRun','all', 'NumTrialPoints', 1000, 'NumStageOnePoints', 200);

    [x2,F2,solutions] = run(gs,gsproblem);

    I get nice estimates of x2.
    So far so good.

    Next I generate yhat (predicted y) based on the model estimate of x2 and the formula.

    yhat = (1 + x2(1)*(x2(2)/0.0025662))*X(:,1) + (x2(2)/x2(3))*(sqrt(1-x2(1)^2))*X(:,2) + x2(4)*X(:,3) + x2(5)*X(:,4) + x2(6)*X(:,5) + x2(7)*X(:,6) + x2(8)*X(:,7) + x2(9)*X(:,8) + x2(10)*X(:,9) + x2(11)*X(:,10) + x2(12)*X(:,11) + x2(13)*X(:,12) + x2(14)*X(:,13) + x2(15)*X(:,14);

    I then compute the residual vector as

    resid = y - yhat;

    My bootstrapping set-up is as follows:

    I define the number of bootstrap samples:

    nboot = 10;

    Then create 10 column vectors of bootstrap indices:

    [~, bootIndices] = bootstrp(nboot, [], resid);

    I then define the 18026 by 10 matrix of 10 residual column vectors:

    bootresid = resid(bootIndices);

    I then define the 18026 by 10 matrix of 10 pseudo-y vectors based on the bootstrapped residual vectors.

    yboot = (1 + x2(1)*(x2(2)/0.0025662))*X(:,1) + (x2(2)/x2(3))*(sqrt(1-x2(1)^2))*X(:,2) + x2(4)*X(:,3) + x2(5)*X(:,4) + x2(6)*X(:,5) + x2(7)*X(:,6) + x2(8)*X(:,7) + x2(9)*X(:,8) + x2(10)*X(:,9) + x2(11)*X(:,10) + x2(12)*X(:,11) + x2(13)*X(:,12) + x2(14)*X(:,13) + x2(15)*X(:,14) + bootresid;

    I initialize my parameter matrix of 10 rows and 15 columns to be a matrix of zeros.

    xb = zeros([10 15]);

    I modify my original function to accommodate yboot (instead of y) and xb instead of x2

    function Fboot = mybootfun(xb,yboot,X)
    Fboot = sum((((yboot - (1 + xb(1)*(xb(2)/0.0025662))*X(:,1) - (xb(2)/xb(3))*(sqrt(1-xb(1)^2))*X(:,2) - xb(4)*X(:,3) - xb(5)*X(:,4) - xb(6)*X(:,5) - xb(7)*X(:,6) - xb(8)*X(:,7) - xb(9)*X(:,8) - xb(10)*X(:,9) - xb(11)*X(:,10) - xb(12)*X(:,11) - xb(13)*X(:,12) - xb(14)*X(:,13) - xb(15)*X(:,14)))).^2);
    end

    Then I run:

    for i = 1:10
    problem_b = createOptimProblem('fmincon','objective',@(xb) mybootfun(xb(i,:), yboot(:,i), X),'x0',x0,'lb',lb,'ub',ub);
    [xb(i,:),Fboot,solution] = run(gs,problem_b);
    end

Results are below. The first run works.

GlobalSearch stopped because it analyzed all the trial points.

All 15 local solver runs converged with a positive local solver exit flag.

After this, the error message that appears when the do loop increments to 2 is as follows.

Index in position 1 exceeds array bounds (must not exceed 1).

Error in @(xb)mybootfun(xb(i,:),yboot(:,i),X)

Error in fmincon (line 546) initVals.f = feval(funfcn{3},X,varargin{:});

Error in globalsearchnlp

Error in GlobalSearch/run (line 340) globalsearchnlp(FUN,X0,A,B,Aeq,Beq,LB,UB,NONLCON,options,localOptions);

Caused by: Failure in initial objective function evaluation. FMINCON cannot continue. Failure in initial call to fmincon with user-supplied problem structure.

[Alan Weiss]

Please edit your post and apply the {} Code button to the code to help us be able to read it.

Alan Weiss

MATLAB mathematical toolbox documentation

[Srinivasan Rangan]

Thanks Alan. I edited the post following your suggestion. Hope it is more readable now.

Answer 1

[Srinivasan Rangan]

Dear All,

There was a simple solution.

I replaced:

for i = 1:100
    problem_b = createOptimProblem('fmincon','objective',@(xb) mybootfun(xb(i,:),yboot(:,i), X),'x0',x0,'lb',lb,'ub',ub);
    [xb(i,:),Fboot,solution] = run(gs,problem_b);
end

with

for i = 1:100
    problem_b = createOptimProblem('fmincon','objective',@(xb) mybootfun(xb,yboot(:,i), X),'x0',x0,'lb',lb,'ub',ub);
    [xb(i,:),Fboot,solution] = run(gs,problem_b);
end

and that did the trick.

Thanks so much! Srini