Calculation of Hessian matrix in gamultiobj hybrid function

I am trying to optimise set of parameters, I am planning to use gamultiobj hybrid function for optimisation.

I am wondering how can I measure the hessain matrix as output at the optimised parameters?

Thank you

Answer 1

[Matt J]

If you mean that you can't compute the Hessian yourself and wish to do so using finite difference approximations then

https://www.mathworks.com/matlabcentral/fileexchange/13490-adaptive-robust-numerical-differentiation?s_tid=srchtitle

[SM]

Thank you, Matt for your response.

My optimisation problem: I am doing a finite element analysis in ABAQUS, and it requires some coefficient, and at every iteration, I optimise the coefficients in MATLAB and pass it to ABAQUS, then I get the result from ABAQUS and pass it to Matlab, to optimise the coefficient again. Therefore, as you can see, there is no explicit formula for fitness function (objective function) to calculate the derivatives.

My issue is: I want to have a hessian matrix as output using gamultiobj when I use fmincon in hybrid function.

similar to documetation of fmincon

[----------------------,hessian]=fmincon(--)

I am wondering if there is a way to do that?

[Matt J]

I am wondering if there is a way to do that?

Well, you should consider my answer, then. It proposed a possible solution.

[SM]

Thank you, I tried the code (hessian.m) in the file and read the code documentation.

I face the follwing error:

Array indices must be positive integers or logical values.

Error in hessdiag>@(xi)fun(swapelement(x0,ind,xi)) (line 60)
@(xi) fun(swapelement(x0,ind,xi)), ...
    
Error in derivest (line 337)
f_x0(j) = fun(x0(j));

Error in hessdiag (line 60)
@(xi) fun(swapelement(x0,ind,xi)), ...
    

I am not sure whay it is showing this error? since the "ind" is positive.

Do you have any advise on that?