Izvorni znanstveni članak

Convergence of the steepest descent method with line searches and uniformly convex objective in reflexive Banach spaces

Fernando Andrés Gallego orcid.org/0000-0001-8615-4032 ; Instituto de Matematicas, Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brazil
John Jairo Quintero ; PCM Computational Applications, Universidad Nacional de Colombia, Manizales, Colombia
Juan Carlos Riano ; PCM Computational Applications, Universidad Nacional de Colombia, Manizales, Colombia

Sažetak

In this paper, we present some algorithms for unconstrained convex optimization problems. The development and analysis of these methods is carried out in a Banach space setting. We begin by introducing a general framework for achieving global convergence without Lipschitz conditions on the gradient, as usual in the current literature. This paper is an extension to Banach spaces to the analysis of the steepest descent method for convex optimization, most of them in less general spaces.

Ključne riječi

uniformly convex functional; descent methods; step-size estimation; metric of gradient

Hrčak ID:

149780

URI

https://hrcak.srce.hr/149780

Datum izdavanja:

18.12.2015.

Posjeta: 2.618 *