Nonsmooth variational inequalities on Hadamard manifolds. Issue 2 (25th January 2020)

• Record Type: Journal Article
• Authors: Ansari, Qamrul Hasan; Islam, Monirul; Yao, Jen-Chih
• Is Part Of: Applicable analysis. Volume 99:Issue 2(2020)
• Page Start: 340
• Page End: 358
• Publication Date: 2020-01-25
• Subjects: Nonsmooth variational inequalities -- Minty nonsmooth variational inequalities -- existence results -- Hadamard manifolds -- gap functions; 49J40 -- 49J52 -- 47J20; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2018.1495329
• Languages: English
• ISSNs: 0003-6811

Abstract

ABSTRACT: Nonsmooth variational inequality problem (NVIP) and Minty nonsmooth variational inequality problem (MNVIP) in terms of a bifunction are considered in the setting of Hadamard manifolds. We first establish a Browder type fixed point theorem in the setting of Hadamard spaces, and then by using it we prove some existence results for solutions of NVIP and MNVIP. We give some relations among NVIP, MNVIP and nonsmooth optimization problem. The gap functions for NVIP and MNVIP are also studied in the setting of Hadamard manifolds.