An inexact hybrid generalized proximal point algorithm and some new results on the theory of Bregman functions

Citation
Mv. Solodov et Bf. Svaiter, An inexact hybrid generalized proximal point algorithm and some new results on the theory of Bregman functions, MATH OPER R, 25(2), 2000, pp. 214-230
Citations number
41
Categorie Soggetti
Mathematics
Journal title
MATHEMATICS OF OPERATIONS RESEARCH
ISSN journal
0364765X → ACNP
Volume
25
Issue
2
Year of publication
2000
Pages
214 - 230
Database
ISI
SICI code
0364-765X(200005)25:2<214:AIHGPP>2.0.ZU;2-S
Abstract
We present a new Bregman-function-based algorithm which is a modification o f the generalized proximal point method for solving the variational inequal ity problem with a maximal monotone operator. The principal advantage of th e presented algorithm is that it allows a more constructive error tolerance criterion in solving the proximal point subproblems. Furthermore, we elimi nate the assumption of pseudomonotonicity which was, until now, standard in proving convergence for paramonotone operators. Thus we obtain a convergen ce result which is new even for exact generalized proximal point methods. F inally, we present some new results on the theory of Bregman functions. For example, we show that the standard assumption of convergence consistency i s a consequence of the other properties of Bregman functions, and is theref ore superfluous.