Retraction-Based Direct Search Methods for Derivative Free Riemannian Optimization

Abstract Direct search methods represent a robust and reliable class of algorithms for solving black-box optimization problems. In this paper, the application those strategies is exported to Riemannian optimization, wherein minimization be performed with respect variables restricted lie on manifold. More specifically, classic linesearch extrapolated variants direct are considered, tailored devised both smooth nonsmooth functions, by making use retractions. A minimizing objectives manifold without having access (sub)derivatives analyzed first time in literature. Along convergence guarantees, set numerical performance illustrations standard problems provided.