Weak sharpness and finite termination for variational inequalities on Hadamard manifolds

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 the 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

2010 Mathematics Subject Classifications:

• 49J40
• 47H05
• 58D17

Disclosure statement

No potential conflict of interest was reported by the author(s).