MATLAB: Minimization of a function with unknown gradient but known sparsity pattern of its hessian

fminconhessian patternno gradient

Dear colleagues,

is there a fmincon option to minimize a function without the knowledge of its gradient but providing a sparsity pattern of a Hessian?

My function comes from a FEM formulation of an energy in nonlinear mechanics of solids and it is too difficult to differentiate analytically.

However the sparsity pattern of the hessian is easily available though a FEM connectivity of variables.

Is there a way to exploit it efficiently? If I run with 'Algorithm','quasi-newton', it seems not to accept 'HessPattern' option. An alternative would be to obtain an appriximative gradient (can you suggest one?) and use 'Algorithm','trust-region' insteady. Does anyone have experience with it?

Best wishes,

Jan

Best Answer

Sorry, I am afraid that the available options don't work efficiently for your case. The HessPattern option is available only for the 'trust-region-reflective' algorithm, but for that algorithm you need to supply a derivative.

I am not sure what to suggest that you probably have not yet tried. For the default 'interior-point' algorithm you can try using the HessianApproximation option set to 'lbfgs' or {'lbfgs',Positive Integer}, but that does not directly use the sparsity pattern that you know. Or, and this seems crazy, you could code a finite difference gradient in your objective funtion, bypassing MATLAB's internal one, and then you could use the 'trust-region-reflective' algorithm with the HessPattern option. I am not sure that the 'trust-region-reflective' algorithm would satisfy you anyway, as it accepts only bound constraints or only linear equality constraints.

Sorry.

Alan Weiss

MATLAB mathematical toolbox documentation

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