Nonsmooth variational inequalities on Hadamard manifolds

Qamrul Hasan Ansari; Monirul Islam; Jen Chih Yao

doi:10.1080/00036811.2018.1495329

Nonsmooth variational inequalities on Hadamard manifolds

Qamrul Hasan Ansari^*
, Monirul Islam
, Jen Chih Yao

^*Corresponding author for this work

King Fahd University of Petroleum & Minerals

Research output: Contribution to journal › Article › peer-review

105 Scopus citations

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.

Original language	English
Pages (from-to)	340-358
Number of pages	19
Journal	Applicable Analysis
Volume	99
Issue number	2
DOIs	https://doi.org/10.1080/00036811.2018.1495329
State	Published - 25 Jan 2020

Bibliographical note

Publisher Copyright:
© 2018, © 2018 Informa UK Limited, trading as Taylor & Francis Group.

Keywords

47J20
49J40
49J52
Hadamard manifolds
Minty nonsmooth variational inequalities
Nonsmooth variational inequalities
existence results
gap functions

ASJC Scopus subject areas

Analysis
Applied Mathematics

Access to Document

10.1080/00036811.2018.1495329

Cite this

@article{daf79e8f291843d5a273a46c3b77a554,

title = "Nonsmooth variational inequalities on Hadamard manifolds",

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.",

keywords = "47J20, 49J40, 49J52, Hadamard manifolds, Minty nonsmooth variational inequalities, Nonsmooth variational inequalities, existence results, gap functions",

author = "Ansari, \{Qamrul Hasan\} and Monirul Islam and Yao, \{Jen Chih\}",

note = "Publisher Copyright: {\textcopyright} 2018, {\textcopyright} 2018 Informa UK Limited, trading as Taylor \& Francis Group.",

year = "2020",

month = jan,

day = "25",

doi = "10.1080/00036811.2018.1495329",

language = "English",

volume = "99",

pages = "340--358",

journal = "Applicable Analysis",

issn = "0003-6811",

number = "2",

}

TY - JOUR

T1 - Nonsmooth variational inequalities on Hadamard manifolds

AU - Ansari, Qamrul Hasan

AU - Islam, Monirul

AU - Yao, Jen Chih

PY - 2020/1/25

Y1 - 2020/1/25

N2 - 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.

AB - 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.

KW - 47J20

KW - 49J40

KW - 49J52

KW - Hadamard manifolds

KW - Minty nonsmooth variational inequalities

KW - Nonsmooth variational inequalities

KW - existence results

KW - gap functions

UR - https://www.scopus.com/pages/publications/85052118625

U2 - 10.1080/00036811.2018.1495329

DO - 10.1080/00036811.2018.1495329

M3 - Article

AN - SCOPUS:85052118625

SN - 0003-6811

VL - 99

SP - 340

EP - 358

JO - Applicable Analysis

JF - Applicable Analysis

IS - 2

ER -

Nonsmooth variational inequalities on Hadamard manifolds

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Fingerprint

Cite this