Constraint qualifications and optimality conditions for nonsmooth multiobjective mathematical programming problems with vanishing constraints on Hadamard manifolds via convexificators

In this paper, we introduce the notion of convexificators in the framework of Hadamard manifolds. We derive some calculus rules for convexificators on Hadamard manifolds and employ them to investigate nonsmooth multiobjective programming problems with vanishing constraints on Hadamard manifolds (abb...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications Vol. 542; no. 2; p. 128873
Main Authors: Upadhyay, B.B., Ghosh, Arnav, Kanzi, Nader
Format: Journal Article
Language:English
Published: Elsevier Inc 15.02.2025
Subjects:
Constraint qualifications
Convexificators
Hadamard manifolds
Vanishing constraints
Hadamard manifolds
Vanishing constraints
Convexificators
Constraint qualifications
ISSN:0022-247X
Online Access:Get full text
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Summary:In this paper, we introduce the notion of convexificators in the framework of Hadamard manifolds. We derive some calculus rules for convexificators on Hadamard manifolds and employ them to investigate nonsmooth multiobjective programming problems with vanishing constraints on Hadamard manifolds (abbreviated as, (NMPVC)). The Abadie constraint qualification (abbreviated as, (ACQ)), as well as the generalized (ACQ) (abbreviated as, (GACQ)), are introduced for (NMPVC) in terms of convexificators. Further, (GACQ) is employed to establish the well-known Karush-Kuhn-Tucker (abbreviated as, KKT) type necessary Pareto efficiency criteria for (NMPVC). Moreover, we introduce several other constraint qualifications for (NMPVC) in the Hadamard manifold setting using convexificators and establish interrelations among them. We have furnished non-trivial examples in the framework of some well-known Hadamard manifolds to illustrate the significance of our results. As far as the best of our knowledge is concerned, constraint qualifications and optimality conditions for (NMPVC) have not yet been studied in the framework of Hadamard manifolds via convexificators.
ISSN:0022-247X
DOI:10.1016/j.jmaa.2024.128873