Constraint Qualifications and Optimality Criteria for Nonsmooth Multiobjective Programming Problems on Hadamard Manifolds

This article deals with a class of constrained nonsmooth multiobjective programming problems (NMOPP) in the setting of Hadamard manifolds. The generalized Guignard constraint qualification (GGCQ), Abadie constraint qualification (ACQ), and the generalized ACQ (GACQ) are introduced in the framework o...

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Published in:	Journal of optimization theory and applications Vol. 200; no. 2; pp. 794 - 819
Main Authors:	Upadhyay, Balendu Bhooshan, Ghosh, Arnav, Treanţă, Savin
Format:	Journal Article
Language:	English
Published:	New York Springer US 01.02.2024 Springer Nature B.V
Subjects:	Applications of Mathematics Applied mathematics Banach spaces Calculus of Variations and Optimal Control; Optimization Constraints Convex analysis Engineering Euclidean space Geometry Manifolds Mathematical programming Mathematics Mathematics and Statistics Multiple objective analysis Operations Research/Decision Theory Optimality criteria Optimization Pareto optimum Qualifications Theory of Computation Optimality conditions 90C30 90C46 Constraint qualifications Hadamard manifolds 90C29 90C48 Mathematical programming
ISSN:	0022-3239, 1573-2878
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Abstract	This article deals with a class of constrained nonsmooth multiobjective programming problems (NMOPP) in the setting of Hadamard manifolds. The generalized Guignard constraint qualification (GGCQ), Abadie constraint qualification (ACQ), and the generalized ACQ (GACQ) are introduced in the framework of Hadamard manifolds for NMOPP using the notion of Clarke subdifferentials. Subsequently, by employing GGCQ and geodesic quasiconvexity assumptions, we establish Karush–Kuhn–Tucker (abbreviated as, KKT)-type necessary criteria of Pareto efficiency for NMOPP. Moreover, we establish that ACQ and GACQ are sufficient criteria for satisfaction of GGCQ. Several nontrivial numerical examples are furnished in manifold settings to demonstrate the validity of the derived results. To the best of our knowledge, this is the first time that ACQ, GACQ, GGCQ, and KKT-type necessary criteria of Pareto efficiency for NMOPP have been studied in manifold setting using Clarke subdifferentials.
AbstractList	This article deals with a class of constrained nonsmooth multiobjective programming problems (NMOPP) in the setting of Hadamard manifolds. The generalized Guignard constraint qualification (GGCQ), Abadie constraint qualification (ACQ), and the generalized ACQ (GACQ) are introduced in the framework of Hadamard manifolds for NMOPP using the notion of Clarke subdifferentials. Subsequently, by employing GGCQ and geodesic quasiconvexity assumptions, we establish Karush–Kuhn–Tucker (abbreviated as, KKT)-type necessary criteria of Pareto efficiency for NMOPP. Moreover, we establish that ACQ and GACQ are sufficient criteria for satisfaction of GGCQ. Several nontrivial numerical examples are furnished in manifold settings to demonstrate the validity of the derived results. To the best of our knowledge, this is the first time that ACQ, GACQ, GGCQ, and KKT-type necessary criteria of Pareto efficiency for NMOPP have been studied in manifold setting using Clarke subdifferentials.
Author	Upadhyay, Balendu Bhooshan Treanţă, Savin Ghosh, Arnav
Author_xml	– sequence: 1 givenname: Balendu Bhooshan surname: Upadhyay fullname: Upadhyay, Balendu Bhooshan organization: Department of Mathematics, Indian Institute of Technology Patna – sequence: 2 givenname: Arnav surname: Ghosh fullname: Ghosh, Arnav organization: Department of Mathematics, Indian Institute of Technology Patna – sequence: 3 givenname: Savin orcidid: 0000-0001-8209-3869 surname: Treanţă fullname: Treanţă, Savin email: savin.treanta@upb.ro organization: Department of Applied Mathematics, University Politehnica of Bucharest, Academy of Romanian Scientists, 54 Splaiul Independentei, Fundamental Sciences Applied in Engineering Research Center (SFAI), University Politehnica of Bucharest
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SubjectTerms	Applications of Mathematics Applied mathematics Banach spaces Calculus of Variations and Optimal Control; Optimization Constraints Convex analysis Engineering Euclidean space Geometry Manifolds Mathematical programming Mathematics Mathematics and Statistics Multiple objective analysis Operations Research/Decision Theory Optimality criteria Optimization Pareto optimum Qualifications Theory of Computation
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Title	Constraint Qualifications and Optimality Criteria for Nonsmooth Multiobjective Programming Problems on Hadamard Manifolds
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