Error bound analysis for vector equilibrium problems with partial order provided by a polyhedral cone

Nguyen Van Hung (), Vicente Novo () and Vo Minh Tam ()
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Nguyen Van Hung: Posts and Telecommunications Institute of Technology
Vicente Novo: Universidad Nacional de Educación a Distancia
Vo Minh Tam: Dong Thap University

Journal of Global Optimization, 2022, vol. 82, issue 1, No 7, 139-159

Abstract: Abstract The aim of this paper is to establish new results on the error bounds for a class of vector equilibrium problems with partial order provided by a polyhedral cone generated by some matrix. We first propose some regularized gap functions of this problem using the concept of $$\mathcal {G}_{A}$$ G A -convexity of a vector-valued function. Then, we derive error bounds for vector equilibrium problems with partial order given by a polyhedral cone in terms of regularized gap functions under some suitable conditions. Finally, a real-world application to a vector network equilibrium problem is given to illustrate the derived theoretical results.

Keywords: Vector equilibrium problem; Vector network equilibrium problem; Regularized gap function; Error bound; Polyhedral cone; 90C30; 90C26; 49J52 (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10898-021-01056-5

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