Generating set search methods for piecewise smooth problems

We consider a direct search approach for solving nonsmooth minimization problems where the objective function is locally Lipschitz continuous and piecewise continuously differentiable on a finite family of polyhedra. A generating set search method is proposed, which is named “structured” because the structure of the set of nondifferentiability near the current iterate is exploited to … Read more

Using Partial Separability of Functions in Generating Set Search Methods for Unconstrained Optimisation

Generating set Search Methods (GSS), a class of derivative-free methods for unconstrained optimisation, are in general robust but converge slowly. It has been shown that the performance of these methods can be enhanced by utilising accumulated information about the objective function as well as a priori knowledge such as partial separability. This paper introduces a … Read more

A generating set search method exploiting curvature and sparsity

Generating Set Search method are one of the few alternatives for optimising high fidelity functions with numerical noise. These methods are usually only efficient when the number of variables is relatively small. This paper presents a modification to an existing Generating Set Search method, which makes it aware of the sparsity structure of the Hessian. … Read more