English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Direct search methods represent a robust and reliable class of algorithms forsolving black-box optimization problems.  In this paper, we explore the application of those strategies to Riemannianoptimization, wherein minimization is to be performed with respect to variablesrestricted to lie on a manifold. More specifically, we consider classic andline search extrapolated variants of direct search, and, by making use ofretractions, we devise tailored strategies for the minimization of both smoothand nonsmooth functions.  As such we analyze, for the first time in the literature, a class ofretraction based algorithms for minimizing nonsmooth objectives on a Riemannianmanifold without having access to (sub)derivatives. Along with convergenceguarantees we provide a set of numerical performance illustrations on astandard set of problems.

Retraction based Direct Search Methods for Derivative Free Riemannian Optimization