Using simplex gradients of nonsmooth functions in direct search methods

Using Simplex Gradients of Nonsmooth Functions in Direct Search Methods

It has been shown recently that the efficiency of direct search methods that use opportunistic polling in positive spanning directions can be improved significantly by reordering the poll directions according to descent indicators built from simplex gradients. The purpose of this paper is twofold. First, we analyze the properties of simplex gradients of nonsmooth functions in the context of dir...

Direct Search Generalized Simplex Algorithm for Optimizing Non-linear Functions

review of radiographic methods in dental implantology

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Smoothing and Worst-Case Complexity for Direct-Search Methods in Nonsmooth Optimization

In the context of the derivative-free optimization of a smooth objective function, it has been shown that the worst case complexity of direct-search methods is of the same order as the one of steepest descent for derivative-based optimization, more precisely that the number of iterations needed to reduce the norm of the gradient of the objective function below a certain threshold is proportiona...

Using Sampling and Simplex Derivatives in Pattern Search Methods

Pattern search methods can be made more efficient if past function evaluations are appropriately reused. In this paper we will introduce a number of ways of reusing previous evaluations of the objective function based on the computation of simplex derivatives (e.g., simplex gradients) to improve the efficiency of a pattern search iteration. At each iteration of a pattern search method, one can ...