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https://hdl.handle.net/10316/44582
Título: | Trust-Region Methods Without Using Derivatives: Worst Case Complexity and the NonSmooth Case | Autor: | Garmanjani, Rohollah Júdice, Diogo Vicente, Luís Nunes |
Data: | 2016 | Editora: | Society for Industrial and Applied Mathematics (SIAM) | Projeto: | info:eu-repo/grantAgreement/FCT/COMPETE/132981/PT | Título da revista, periódico, livro ou evento: | SIAM Journal on Optimization | Volume: | 26 | Número: | 4 | Resumo: | Trust-region methods are a broad class of methods for continuous optimization that found application in a variety of problems and contexts. In particular, they have been studied and applied for problems without using derivatives. The analysis of trust-region derivative-free methods has focused on global convergence, and they have been proven to generate a sequence of iterates converging to stationarity independently of the starting point. Most of such an analysis is carried out in the smooth case, and, moreover, little is known about the complexity or global rate of these methods. In this paper, we start by analyzing the worst case complexity of general trust-region derivative-free methods for smooth functions. For the nonsmooth case, we propose a smoothing approach, for which we prove global convergence and bound the worst case complexity effort. For the special case of nonsmooth functions that result from the composition of smooth and nonsmooth/convex components, we show how to improve the existing results of the literature and make them applicable to the general methodology. | URI: | https://hdl.handle.net/10316/44582 | DOI: | 10.1137/151005683 10.1137/151005683 |
Direitos: | openAccess |
Aparece nas coleções: | I&D CMUC - Artigos em Revistas Internacionais |
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