Nonsmooth variational-like inequalities and nonsmooth vector optimization

M. Alshahrani; Q. H. Ansari; S. Al-Homidan

doi:10.1007/s11590-013-0614-9

Nonsmooth variational-like inequalities and nonsmooth vector optimization

M. Alshahrani, Q. H. Ansari, S. Al-Homidan

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

7 Scopus citations

Abstract

In this paper, we consider nonsmooth vector variational-like inequalities and nonsmooth vector optimization problems. By using the scalarization method, we define nonsmooth variational-like inequalities by means of Clarke generalized directional derivative and study their relations with the vector optimizations and the scalarized optimization problems. Some existence results for solutions of our nonsmooth variational-like inequalities are presented under densely pseudomonotonicity or pseudomonotonicity assumption.

Original language	English
Pages (from-to)	739-751
Number of pages	13
Journal	Optimization Letters
Volume	8
Issue number	2
DOIs	https://doi.org/10.1007/s11590-013-0614-9
State	Published - Feb 2014

Bibliographical note

Funding Information:
Acknowledgments This research was done during the stay of second author at King Fahd University of Petroleum & Minerals, Dhahran Saudi Arabia. It was supported by a KFUPM funded project No. IN 101009.

Keywords

Densely pseudomonotonicity
Existence results
Nonsmooth variational-like inequalities
Nonsmooth vector optimization
Nonsmooth vector variational-like inequalities
Scalarization

ASJC Scopus subject areas

Control and Optimization

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10.1007/s11590-013-0614-9

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abstract = "In this paper, we consider nonsmooth vector variational-like inequalities and nonsmooth vector optimization problems. By using the scalarization method, we define nonsmooth variational-like inequalities by means of Clarke generalized directional derivative and study their relations with the vector optimizations and the scalarized optimization problems. Some existence results for solutions of our nonsmooth variational-like inequalities are presented under densely pseudomonotonicity or pseudomonotonicity assumption.",

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author = "M. Alshahrani and Ansari, \{Q. H.\} and S. Al-Homidan",

note = "Funding Information: Acknowledgments This research was done during the stay of second author at King Fahd University of Petroleum \& Minerals, Dhahran Saudi Arabia. It was supported by a KFUPM funded project No. IN 101009.",

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AU - Ansari, Q. H.

AU - Al-Homidan, S.

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N2 - In this paper, we consider nonsmooth vector variational-like inequalities and nonsmooth vector optimization problems. By using the scalarization method, we define nonsmooth variational-like inequalities by means of Clarke generalized directional derivative and study their relations with the vector optimizations and the scalarized optimization problems. Some existence results for solutions of our nonsmooth variational-like inequalities are presented under densely pseudomonotonicity or pseudomonotonicity assumption.

AB - In this paper, we consider nonsmooth vector variational-like inequalities and nonsmooth vector optimization problems. By using the scalarization method, we define nonsmooth variational-like inequalities by means of Clarke generalized directional derivative and study their relations with the vector optimizations and the scalarized optimization problems. Some existence results for solutions of our nonsmooth variational-like inequalities are presented under densely pseudomonotonicity or pseudomonotonicity assumption.

KW - Densely pseudomonotonicity

KW - Existence results

KW - Nonsmooth variational-like inequalities

KW - Nonsmooth vector optimization

KW - Nonsmooth vector variational-like inequalities

KW - Scalarization

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JO - Optimization Letters

JF - Optimization Letters

IS - 2

ER -

Nonsmooth variational-like inequalities and nonsmooth vector optimization

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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