On Constraint Qualifications for Mathematical Programming Problems with Vanishing Constraints on Hadamard Manifolds

Balendu Bhooshan Upadhyay () and Arnav Ghosh ()
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Balendu Bhooshan Upadhyay: Indian Institute of Technology Patna
Arnav Ghosh: Indian Institute of Technology Patna

Journal of Optimization Theory and Applications, 2023, vol. 199, issue 1, No 1, 35 pages

Abstract: Abstract This article is devoted to the study of mathematical programming problems with vanishing constraints on Hadamard manifolds (in short, MPVC-HM). We present the Abadie constraint qualification (in short, ACQ) and (MPVC-HM)-tailored ACQ for MPVC-HM and provide some necessary conditions for the satisfaction of ACQ for MPVC-HM. Moreover, we demonstrate that the Guignard constraint qualification (in short, GCQ) is satisfied for MPVC-HM under certain mild restrictions. We introduce several (MPVC-HM)-tailored constraint qualifications in the framework of Hadamard manifolds that ensure satisfaction of GCQ. Moreover, we refine our analysis and present some modified sufficient conditions which guarantee that GCQ is satisfied. Several non-trivial examples are incorporated to illustrate the significance of the derived results. To the best of our knowledge, constraint qualifications for mathematical programming problems with vanishing constraints in manifold setting have not been explored before.

Keywords: Mathematical programming; Constraint qualifications; Vanishing constraints; Hadamard manifolds; 90C34; 90C46; 90C48; 90C29 (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (5)

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DOI: 10.1007/s10957-023-02207-2

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