Proximal Methods with Bregman Distances to Solve VIP on Hadamard Manifolds with Null Sectional Curvature

Erik Alex Papa Quiroz, Paulo Roberto Oliveira

Research output: Contribution to journalArticlepeer-review

Abstract

We present an extension of the proximal point method with Bregman distances to solve variational inequality problems (VIP) on Hadamard manifolds with null sectional curvature. Under some natural assumptions, as for example, the existence of solutions of the VIP and the monotonicity of the multivalued vector field, we prove that the sequence of the iterates given by the method converges to a solution of the problem. Furthermore, this convergence is linear or superlinear with respect to the Bregman distance.

Original languageEnglish
JournalJournal of the Operations Research Society of China
DOIs
StateAccepted/In press - 2020
Externally publishedYes

Keywords

  • Bregman distances
  • Hadamard manifolds
  • Monotone vector field
  • Proximal point methods
  • Variational inequality problems

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