Higher-Order Radial Hadamard Directional Derivatives and Applications to Set-Valued Equilibrium Problems

Tian Tang () and Guolin Yu
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Tian Tang: School of Mathematics and Statistics, Ningxia University, Yinchuan, Ningxia 750021, P. R. China
Guolin Yu: Institute of Applied Mathematics, North Minzu University, Yinchuan, Ningxia 750021, P. R. China

Asia-Pacific Journal of Operational Research (APJOR), 2024, vol. 41, issue 06, 1-24

Abstract: In this paper, we first introduce the higher-order lower and upper radial Hadamard directional derivatives for set-valued maps, which can capture the global information of concerning maps, and discuss the relationships with other existed higher-order derivatives. Second, based on the introduced derivatives, we establish optimality conditions for Henig efficient solutions of a set-valued equilibrium problem with constraints. Particularly, the optimality conditions hold in the case where the derivatives of objective and constraint functions are separated. Finally, we give some duality theorems for a mixed type of primal-dual set-valued equilibrium problem. The main results of this paper are illustrated by several concrete examples.

Keywords: Higher-order radial Hadamard directional derivative; set-valued equilibrium problem; Henig efficient solution; optimality condition; duality (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S0217595924500064

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