Vector variational inequalities on Hadamard manifolds involving strongly geodesic convex functions

Anurag Jayswal; Izhar Ahmad; Babli Kumari

doi:10.1016/j.orl.2019.01.004

Vector variational inequalities on Hadamard manifolds involving strongly geodesic convex functions

Anurag Jayswal, Izhar Ahmad, Babli Kumari^*

^*Corresponding author for this work

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

7 Scopus citations

Abstract

This paper is intended to study the vector variational inequalities on Hadamard manifolds. Generalized Minty and Stampacchia vector variational inequalities are introduced involving generalized subdifferential. Under strongly geodesic convexity, relations between solutions of these inequalities and a nonsmooth vector optimization problem are established. To illustrate the relationship between a solution of generalized weak Stampacchia vector variational inequality and weak efficiency of a nonsmooth vector optimization problem, a non-trivial example is presented.

Original language	English
Pages (from-to)	110-114
Number of pages	5
Journal	Operations Research Letters
Volume	47
Issue number	2
DOIs	https://doi.org/10.1016/j.orl.2019.01.004
State	Published - Mar 2019

Bibliographical note

Funding Information:
The authors are thankful to referees for their valuable remarks which improved the results and presentation of this article. This work is financially supported by the Council of Scientific and Industrial Research, New Delhi, India through Grant No.: 25(0266)/17/EMR-II.

Funding Information:
The authors are thankful to referees for their valuable remarks which improved the results and presentation of this article. This work is financially supported by the Council of Scientific and Industrial Research, New Delhi, India through Grant No.: 25(0266)/17/EMR-II .

Publisher Copyright:
© 2019

Keywords

Generalized subdifferential
Hadamard manifold
Strongly geodesic convexity
Vector optimization problem
Vector variational inequality

ASJC Scopus subject areas

Software
Management Science and Operations Research
Industrial and Manufacturing Engineering
Applied Mathematics

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10.1016/j.orl.2019.01.004

Cite this

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title = "Vector variational inequalities on Hadamard manifolds involving strongly geodesic convex functions",

abstract = "This paper is intended to study the vector variational inequalities on Hadamard manifolds. Generalized Minty and Stampacchia vector variational inequalities are introduced involving generalized subdifferential. Under strongly geodesic convexity, relations between solutions of these inequalities and a nonsmooth vector optimization problem are established. To illustrate the relationship between a solution of generalized weak Stampacchia vector variational inequality and weak efficiency of a nonsmooth vector optimization problem, a non-trivial example is presented.",

keywords = "Generalized subdifferential, Hadamard manifold, Strongly geodesic convexity, Vector optimization problem, Vector variational inequality",

author = "Anurag Jayswal and Izhar Ahmad and Babli Kumari",

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AU - Jayswal, Anurag

AU - Ahmad, Izhar

AU - Kumari, Babli

N1 - Funding Information: The authors are thankful to referees for their valuable remarks which improved the results and presentation of this article. This work is financially supported by the Council of Scientific and Industrial Research, New Delhi, India through Grant No.: 25(0266)/17/EMR-II. Funding Information: The authors are thankful to referees for their valuable remarks which improved the results and presentation of this article. This work is financially supported by the Council of Scientific and Industrial Research, New Delhi, India through Grant No.: 25(0266)/17/EMR-II . Publisher Copyright: © 2019

PY - 2019/3

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N2 - This paper is intended to study the vector variational inequalities on Hadamard manifolds. Generalized Minty and Stampacchia vector variational inequalities are introduced involving generalized subdifferential. Under strongly geodesic convexity, relations between solutions of these inequalities and a nonsmooth vector optimization problem are established. To illustrate the relationship between a solution of generalized weak Stampacchia vector variational inequality and weak efficiency of a nonsmooth vector optimization problem, a non-trivial example is presented.

AB - This paper is intended to study the vector variational inequalities on Hadamard manifolds. Generalized Minty and Stampacchia vector variational inequalities are introduced involving generalized subdifferential. Under strongly geodesic convexity, relations between solutions of these inequalities and a nonsmooth vector optimization problem are established. To illustrate the relationship between a solution of generalized weak Stampacchia vector variational inequality and weak efficiency of a nonsmooth vector optimization problem, a non-trivial example is presented.

KW - Generalized subdifferential

KW - Hadamard manifold

KW - Strongly geodesic convexity

KW - Vector optimization problem

KW - Vector variational inequality

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DO - 10.1016/j.orl.2019.01.004

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SN - 0167-6377

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JO - Operations Research Letters

JF - Operations Research Letters

IS - 2

ER -

Vector variational inequalities on Hadamard manifolds involving strongly geodesic convex functions

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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