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Weak sharpness and finite termination for variational inequalities on Hadamard manifolds

Nguyen Luong(luonghdu***at***gmail.com)

Abstract: We first introduce the notion of weak sharpness for the solution sets of variational inequality problems (in short, VIP) on Hadamard spaces. We then study the finite convergence property of sequences generated by the inexact proximal point algorithm with different error terms for solving VIP under weak sharpness of the solution set. We also give an upper bound on the number of iterations by which the sequence generated by exact proximal point algorithm converges to a solution of VIP. An example is also given to illustrate our results.

Keywords: Variational inequalities; Proximal point algorithm; Weak sharpness; Finite termination; Hadamard manifolds

Category 1: Nonlinear Optimization

Citation: 15 pages

Download: [PDF]

Entry Submitted: 08/24/2019
Entry Accepted: 08/25/2019
Entry Last Modified: 08/24/2019

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