Paper's Title:

Constraint Qualifications for Multiobjective Programming Problems on Hadamard Manifolds

Author(s):

Arnav Ghosh, Balendu Bhooshan Upadhyay and I.M. Stancu-Minasian

Department of Mathematics,
Indian Institute of Technology Patna,
Patna,
India.
E-mail: arnav_2021ma09@iitp.ac.in

Department of Mathematics,
Indian Institute of Technology Patna,
Patna,
India.
E-mail: bhooshan@iitp.ac.in

"Gheorghe Mihoc-Caius Iacob" Institute of Mathematical Statistics and Applied Mathematics of the Romanian Academy,
Bucharest,
Romania.
E-mail: stancu_minasian@yahoo.com 

Abstract:

The study of optimization methods on manifolds has emerged as an immensely significant topic in mathematics due its ubiquitous applicability as well as various computational advantages associated with it. Motivated by this fact, the present article is devoted to the study of a class of constrained multiobjective programming problems (MOPP) in the framework of Hadamard manifolds. We present the generalized Guignard constraint qualification (GGCQ) in the framework of Hadamard manifolds for (MOPP). Employing (GGCQ), we derive Karush-Kuhn-Tucker type necessary optimality criteria for (MOPP). Moreover, we present several other constraint qualifications (CQs) on Hadamard manifolds, namely, Abadie's CQ, generalized Abadie's CQ, Cottle-type CQ, Slater-type CQ, linear CQ, linear objective CQ and Mangasarian-Fromovitz CQ. Further, we establish various relations between these constraint qualifications. In particular, we show that these constraint qualifications, in turn, become sufficient conditions ensuring that (GGCQ) is satisfied.

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