The Tikhonov regularization for vector equilibrium problems

Lam Quoc Anh (), Tran Quoc Duy (), Le Dung Muu () and Truong Van Tri ()
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Lam Quoc Anh: Cantho University
Tran Quoc Duy: FPT University
Le Dung Muu: Thang Long University
Truong Van Tri: University of Ostrava

Computational Optimization and Applications, 2021, vol. 78, issue 3, No 4, 769-792

Abstract: Abstract We consider vector equilibrium problems in real Banach spaces and study their regularized problems. Based on cone continuity and generalized convexity properties of vector-valued mappings, we propose general conditions that guarantee existence of solutions to such problems in cases of monotonicity and nonmonotonicity. First, our study indicates that every Tikhonov trajectory converges to a solution to the original problem. Then, we establish the equivalence between the problem solvability and the boundedness of any Tikhonov trajectory. Finally, the convergence of the Tikhonov trajectory to the least-norm solution of the original problem is discussed.

Keywords: Tikhonov regularization; Vector equilibrium problem; Tikhonov trajectory; Least-norm solution; Generalized Archimedean axiom; 49J53; 65J20; 90C33 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10589-020-00258-z

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