Equal Angle Distribution of Polling Directions in Direct-Search Methods

Abstract EN

The purpose of this paper is twofold: first, to introduce deterministic strategies for directional direct-search methods, including new instances of the mesh adaptive direct-search (Mads) and the generating set search (Gss) class of algorithms, which utilize a nice distribution of Poll directions when compared to other strategies, and second, to introduce variants of each algorithm which utilize a minimal positive basis at each step.

The strategies base their Poll directions on the use of the QR decomposition to obtain an orthogonal set of directions or on using the equal angular directions from a regular simplex centered at the origin with vertices on the unit sphere.

Test results are presented on a set of smooth, nonsmooth, unconstrained, and constrained problems that give comparisons between the various implementations of these directional direct-search methods.