An interior point method with Bregman functions for the variational inequality problem with paramonotone operators

作     者：Censor, Y Iusem, AN Zenios, SA 

作者机构：Univ Haifa Dept Math IL-31905 Haifa Israel Inst Matematica Pura & Aplicada BR-22460 Rio De Janeiro Brazil Univ Cyprus Dept Publ & Business Adm Nicosia Cyprus 

出 版 物：《MATHEMATICAL PROGRAMMING》 (数学规划)

年 卷 期：1998年第81卷第3期

页      面：373-400页

核心收录：

学科分类：1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 070104[理学-应用数学] 0835[工学-软件工程] 0701[理学-数学] 

基　　金：Department of Radiology National Science Foundation, NSF, (CCR-91-04042) National Institutes of Health, NIH, (HL-28438) Wharton School, University of Pennsylvania Conselho Nacional de Desenvolvimento Científico e Tecnológico, CNPq, (301280/86) 

主　　题：variational inequalities monotone operators paramonotone operators convex programming generalized distances 

摘      要：We present an algorithm for the variational inequality problem on convex sets with nonempty interior. The use of Bregman functions whose zone is the convex set allows for the generation of a sequence contained in the interior, without taking explicitly into account the constraints which define the convex set. We establish full convergence to a solution with minimal conditions upon the monotone operator F, weaker than strong monotonicity or Lipschitz continuity, for instance, and including cases where the solution needs not be unique. We apply our algorithm to several relevant classes of convex sets, including orthants, boxes, polyhedra and balls, for which Bregman functions are presented which give rise to explicit iteration formulae, up to the determination of two scalar stepsizes, which can be found through finite search procedures. (C) 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.