Minty Variational Principle for Nonsmooth Interval-Valued Vector Optimization Problems on Hadamard Manifolds

Savin Treanţă, Priyanka Mishra and Balendu Bhooshan Upadhyay
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Savin Treanţă: Department of Applied Mathematics, University Politehnica of Bucharest, 060042 Bucharest, Romania
Priyanka Mishra: Department of Mathematics, Indian Institute of Technology Patna, Patna 801103, Bihar, India
Balendu Bhooshan Upadhyay: Department of Mathematics, Indian Institute of Technology Patna, Patna 801103, Bihar, India

Mathematics, 2022, vol. 10, issue 3, 1-15

Abstract: This article deals with the classes of approximate Minty- and Stampacchia-type vector variational inequalities on Hadamard manifolds and a class of nonsmooth interval-valued vector optimization problems. By using the Clarke subdifferentials, we define a new class of functions on Hadamard manifolds, namely, the geodesic L U -approximately convex functions. Under geodesic L U -approximate convexity hypothesis, we derive the relationship between the solutions of these approximate vector variational inequalities and nonsmooth interval-valued vector optimization problems. This paper extends and generalizes some existing results in the literature.

Keywords: Clarke subdifferentials; geodesic LU -approximately convex functions; Hadamard manifolds (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (2)

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