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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Bibliographic Details
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
Online Access:Get full text
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Summary: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.
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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-023-02301-5