A gap function and existence of solutions for a non-smooth vector variational inequality on Hadamard manifolds

Anurag Jayswal; Babli Kumari; Izhar Ahmad

doi:10.1080/02331934.2020.1759057

A gap function and existence of solutions for a non-smooth vector variational inequality on Hadamard manifolds

Anurag Jayswal, Babli Kumari^*, Izhar Ahmad

^*Corresponding author for this work

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

3 Scopus citations

Abstract

In the present paper, a gap function for a non-smooth mixed weak vector variational inequality involving generalized gradient on Hadamard manifolds is obtained. A non-trivial example is presented to illustrate the relationship between a gap function and a non-smooth mixed weak vector variational inequality. The existence of solution for a non-smooth mixed weak vector variational inequality without monotonicity is also studied. Moreover, a g-pseudomonotone is introduced and it is employed to discuss the existence of solution for an aforesaid problem.

Original language	English
Pages (from-to)	1875-1889
Number of pages	15
Journal	Optimization
Volume	70
Issue number	9
DOIs	https://doi.org/10.1080/02331934.2020.1759057
State	Published - 2021

Bibliographical note

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

Publisher Copyright:
© 2020 Informa UK Limited, trading as Taylor & Francis Group.

Keywords

Hadamard manifold
KKM mapping
Mixed weak vector variational inequality
gap function
generalized monotone

ASJC Scopus subject areas

Control and Optimization
Management Science and Operations Research
Applied Mathematics

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10.1080/02331934.2020.1759057

Cite this

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title = "A gap function and existence of solutions for a non-smooth vector variational inequality on Hadamard manifolds",

abstract = "In the present paper, a gap function for a non-smooth mixed weak vector variational inequality involving generalized gradient on Hadamard manifolds is obtained. A non-trivial example is presented to illustrate the relationship between a gap function and a non-smooth mixed weak vector variational inequality. The existence of solution for a non-smooth mixed weak vector variational inequality without monotonicity is also studied. Moreover, a g-pseudomonotone is introduced and it is employed to discuss the existence of solution for an aforesaid problem.",

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

note = "Funding Information: This work is financially supported by the Council of Scientific and Industrial Research, New Delhi, India through Grant No.: 25(0266)/17/EMR-II. The authors are thankful to referees for their valuable remarks which improved the results and presentation of this article. Publisher Copyright: {\textcopyright} 2020 Informa UK Limited, trading as Taylor & Francis Group.",

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T1 - A gap function and existence of solutions for a non-smooth vector variational inequality on Hadamard manifolds

AU - Jayswal, Anurag

AU - Kumari, Babli

AU - Ahmad, Izhar

N1 - Funding Information: This work is financially supported by the Council of Scientific and Industrial Research, New Delhi, India through Grant No.: 25(0266)/17/EMR-II. The authors are thankful to referees for their valuable remarks which improved the results and presentation of this article. Publisher Copyright: © 2020 Informa UK Limited, trading as Taylor & Francis Group.

PY - 2021

Y1 - 2021

N2 - In the present paper, a gap function for a non-smooth mixed weak vector variational inequality involving generalized gradient on Hadamard manifolds is obtained. A non-trivial example is presented to illustrate the relationship between a gap function and a non-smooth mixed weak vector variational inequality. The existence of solution for a non-smooth mixed weak vector variational inequality without monotonicity is also studied. Moreover, a g-pseudomonotone is introduced and it is employed to discuss the existence of solution for an aforesaid problem.

AB - In the present paper, a gap function for a non-smooth mixed weak vector variational inequality involving generalized gradient on Hadamard manifolds is obtained. A non-trivial example is presented to illustrate the relationship between a gap function and a non-smooth mixed weak vector variational inequality. The existence of solution for a non-smooth mixed weak vector variational inequality without monotonicity is also studied. Moreover, a g-pseudomonotone is introduced and it is employed to discuss the existence of solution for an aforesaid problem.

KW - Hadamard manifold

KW - KKM mapping

KW - Mixed weak vector variational inequality

KW - gap function

KW - generalized monotone

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U2 - 10.1080/02331934.2020.1759057

DO - 10.1080/02331934.2020.1759057

M3 - Article

AN - SCOPUS:85084312163

SN - 0233-1934

VL - 70

SP - 1875

EP - 1889

JO - Optimization

JF - Optimization

IS - 9

ER -

A gap function and existence of solutions for a non-smooth vector variational inequality on Hadamard manifolds

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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