Higher-Order Efficiency Conditions for Continuously Directional Differentiable Vector Equilibrium Problem with Constraints

In this paper, we give optimality conditions of higher-order for a continuously directional differentiable vector equilibrium problem with constraints. First, we obtain some important characterizations and existence results for a m -times continuously directional differentiable function( m is a posi...

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Bibliographic Details
Published inBulletin of the Iranian Mathematical Society Vol. 48; no. 4; pp. 1805 - 1828
Main Author Van Su, Tran
Format Journal Article
LanguageEnglish
Published Singapore Springer Nature Singapore 01.08.2022
Subjects
Mathematics
Mathematics and Statistics
Original Paper
Critical directions
9046C
KKT type higher-order optimality conditions
Efficient solution types
49J52
Higher-order directional derivatives
90C29
90C48
Continuously directional differentiable vector equilibrium problem with constraints
91B50
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Summary:In this paper, we give optimality conditions of higher-order for a continuously directional differentiable vector equilibrium problem with constraints. First, we obtain some important characterizations and existence results for a m -times continuously directional differentiable function( m is a positive integer number). Second, as an application, we provide some higher-order Karush–Kuhn–Tucker necessary optimality conditions for efficiency. Finally, some higher-order sufficient optimality conditions, which are very close to the higher-order Karush–Kuhn–Tucker necessary optimality conditions, are presented as well. Some illustrative examples are also given.
ISSN:1017-060X
1735-8515
DOI:10.1007/s41980-021-00621-8