Convex proximal bundle methods in depth: a unified analysis for inexact oracles
成果类型：
Article
署名作者：
Oliveira, W. de; Sagastizabal, C.; Lemarechal, C.
署名单位：
Instituto Nacional de Matematica Pura e Aplicada (IMPA); Instituto Nacional de Matematica Pura e Aplicada (IMPA); Inria
刊物名称：
MATHEMATICAL PROGRAMMING
ISSN/ISSBN：
0025-5610
DOI：
10.1007/s10107-014-0809-6
发表日期：
2014
页码：
241-277
关键词：
摘要：
The last few years have seen the advent of a new generation of bundle methods, capable to handle inexact oracles, polluted by noise. Proving convergence of a bundle method is never simple and coping with inexact oracles substantially increases the technicalities. Besides, several variants exist to deal with noise, each one needing an ad hoc proof to show convergence. We state a synthetic convergence theory, in which we highlight the main arguments and specify which assumption is used to establish each intermediate result. The framework is comprehensive and generalizes in various ways a number of algorithms proposed in the literature. Based on the ingredients of our synthetic theory, we consider various bundle methods adapted to oracles for which high accuracy is possible, yet it is preferable not to make exact calculations often, because they are too time consuming.