A subgradient algorithm for a class of nonlinear split feasibility problems: application to jointly constrained Nash equilibrium models

Le Hai Yen (), Nguyen Thi Thanh Huyen () and Le Dung Muu ()
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Le Hai Yen: VAST
Nguyen Thi Thanh Huyen: Thainguyen University of Sciences
Le Dung Muu: VAST

Journal of Global Optimization, 2019, vol. 73, issue 4, No 8, 849-868

Abstract: Abstract In this paper we propose an algorithm for solving the split feasibility problem $$x\in C, Ax\in Q$$ x ∈ C , A x ∈ Q with C being the solution set of an equilibrium problem and A can be nonlinear. The proposed algorithm is a combination between the projection method for the equilibrium problem and the gradient method for the inclusion $$Ax\in Q$$ A x ∈ Q . The convergence of the algorithm is investigated. A numerical example for a jointly constrained Nash equilibrium model in electricity production market is provided to demonstrate the behavior of the algorithm.

Keywords: Nonlinear split feasibility; Equilibria; Subgradient method; Quasiconvexity; Nash model (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10898-018-00735-0

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