Constraint Qualifications and Optimality Conditions for Multiobjective Mathematical Programming Problems with Vanishing Constraints on Hadamard Manifolds

Balendu Bhooshan Upadhyay, Arnav Ghosh, Savin Treanţă and Jen-Chih Yao ()
Additional contact information
Balendu Bhooshan Upadhyay: Department of Mathematics, Indian Institute of Technology Patna, Patna 801103, India
Arnav Ghosh: Department of Mathematics, Indian Institute of Technology Patna, Patna 801103, India
Savin Treanţă: Department of Applied Mathematics, National University of Science and Technology POLITEHNICA Bucharest, 060042 Bucharest, Romania
Jen-Chih Yao: Center for General Education, China Medical University, Taichung 40402, Taiwan

Mathematics, 2024, vol. 12, issue 19, 1-24

Abstract: In this paper, we investigate constraint qualifications and optimality conditions for multiobjective mathematical programming problems with vanishing constraints (MOMPVC) on Hadamard manifolds. The MOMPVC-tailored generalized Guignard constraint qualification (MOMPVC-GGCQ) for MOMPVC is introduced in the setting of Hadamard manifolds. By employing MOMPVC-GGCQ and the intrinsic properties of Hadamard manifolds, we establish Karush–Kuhn–Tucker (KKT)-type necessary Pareto efficiency criteria for MOMPVC. Moreover, we introduce several MOMPVC-tailored constraint qualifications and develop interrelations among them. In particular, we establish that the MOMPVC-tailored constraint qualifications introduced in this paper turn out to be sufficient conditions for MOMPVC-GGCQ. Suitable illustrative examples are furnished in the framework of well-known Hadamard manifolds to validate and demonstrate the importance and significance of the derived results. To the best of our knowledge, this is the first time that constraint qualifications, their interrelations, and optimality criteria for MOMPVC have been explored in the framework of Hadamard manifolds.

Keywords: constraint qualifications; multiobjective programming; vanishing constraints; optimality conditions; Hadamard manifolds (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/12/19/3047/pdf (application/pdf)
https://www.mdpi.com/2227-7390/12/19/3047/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:12:y:2024:i:19:p:3047-:d:1488312

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().