DC auxiliary principle methods for solving lexicographic equilibrium problems

Pham Ngoc Anh (), Qamrul Hasan Ansari () and Ho Phi Tu ()
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Pham Ngoc Anh: Posts and Telecommunications Institute of Technology
Qamrul Hasan Ansari: Aligarh Muslim University
Ho Phi Tu: Haiphong University

Journal of Global Optimization, 2023, vol. 85, issue 1, No 7, 129-153

Abstract: Abstract In this paper, we present DC (difference of convex functions) auxiliary principle methods for solving lexicographic equilibrium problems. Under the strongly monotone and Lipchitz-type assumptions of the cost bifunction, we study the convergence of the sequence generated by the proposed algorithms to a unique solution of the considered lexicographic equilibrium problem. Moreover, we also study the asymptotic behavior of the algorithm for solving the considered problem under the presence of computational errors. Finally, we give some numerical experiments to illustrate the behaviour of the proposed algorithms and provide their comparison with some known algorithms.

Keywords: Lexicographic equilibrium problems; Affine variational inequalities; Auxiliary principle; DC functions; Strongly monotonicity; Lipschitz-type condition; 65K05; 65K15; 47J20; 47J25; 90C33; 90C35 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10898-022-01200-9

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