Enlargement of Monotone Vector Fields and an Inexact Proximal Point Method for Variational Inequalities in Hadamard Manifolds

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• 作者：Edvaldo E. A. Batista…
• 关键词：Enlargement of vector fields ; Inexact proximal ; Constrained optimization ; Hadamard manifold ; 90C33 ; 65K05 ; 47J25
• 刊名：Journal of Optimization Theory and Applications
• 出版年：2016
• 出版时间：September 2016
• 年：2016
• 卷：170
• 期：3
• 页码：916-931
• 全文大小：469 KB
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• 作者单位：Edvaldo E. A. Batista (1)
  Glaydston de Carvalho Bento (2)
  Orizon P. Ferreira (2)
  
  1. Universidade Federal do Oeste da Bahia, Barreiras, BA, 47808-021, Brazil
  2. IME, Universidade Federal de Goiás, Goiânia, GO, 74001-970, Brazil
  
• 刊物主题：Calculus of Variations and Optimal Control; Optimization; Optimization; Theory of Computation; Applications of Mathematics; Engineering, general; Operations Research/Decision Theory;
• 出版者：Springer US
• ISSN：1573-2878
• 卷排序：170

文摘

In this paper, an inexact proximal point method for variational inequalities in Hadamard manifolds is introduced and its convergence properties are studied. To present our method, we generalize the concept of enlargement of monotone operators, from a linear setting to the Riemannian context. As an application, an inexact proximal point method for constrained optimization problems is obtained. Keywords Enlargement of vector fields Inexact proximal Constrained optimization Hadamard manifold