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

This paper addresses the study of derivative-free smooth optimizationproblems, where the gradient information on the objective function isunavailable. Two novel general derivative-free methods are proposed anddeveloped for minimizing such functions with either global or local Lipschitzcontinuous gradients. The newly developed methods use gradient approximationsbased on finite differences, where finite difference intervals areautomatically adapted to the magnitude of the exact gradients without knowingthem exactly. The suggested algorithms achieve fundamental convergence results,including stationarity of accumulation points in general settings as well asglobal convergence with constructive convergence rates when the Kurdyka-\Lojasiewicz property is imposed. The local convergence of the proposedalgorithms to nonisolated local minimizers, along with their local convergencerates, is also analyzed under this property. Numerical experiences involvingvarious convex, nonconvex, noiseless, and noisy functions demonstrate that thenew methods exhibit essential advantages over other state-of-the-art methods inderivative-free optimization.

General Derivative-Free Optimization Methods under Global and Local Lipschitz Continuity of Gradients