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

2015/11/26 by E. E. A. Batista, Batista, E. E. A., G. C. Bento +3
Computer Science · Engineering · #65K05 #90C33 #Advanced Numerical Analysis Techniques #Contact Mechanics and Variational Inequalities #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.1511.08301

openalex publication_date 2015/11/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper an inexact proximal point method for variational inequalities in Hadamard manifolds is introduced and studied its convergence properties. The main tool used for presenting the method is the concept of enlargement of monotone vector fields, which generalizes the concept of enlargement of monotone operators from the linear setting to the Riemannian context. As an application, an inexact proximal point method for constrained optimization problems is obtained.

Citations

• The proximal point algorithm in metric spaces

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