A Projected Subgradient Algorithm for Bilevel Equilibrium Problems and Applications

Le Quang Thuy () and Trinh Ngoc Hai ()
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Le Quang Thuy: Hanoi University of Science and Technology
Trinh Ngoc Hai: Hanoi University of Science and Technology

Journal of Optimization Theory and Applications, 2017, vol. 175, issue 2, No 6, 431 pages

Abstract: Abstract In this paper, we propose a new algorithm for solving a bilevel equilibrium problem in a real Hilbert space. In contrast to most other projection-type algorithms, which require to solve subproblems at each iteration, the subgradient method proposed in this paper requires only to calculate, at each iteration, two subgradients of convex functions and one projection onto a convex set. Hence, our algorithm has a low computational cost. We prove a strong convergence theorem for the proposed algorithm and apply it for solving the equilibrium problem over the fixed point set of a nonexpansive mapping. Some numerical experiments and comparisons are given to illustrate our results. Also, an application to Nash–Cournot equilibrium models of a semioligopolistic market is presented.

Keywords: Bilevel equilibrium problems; Subgradient method; Projection method; Strong monotonicity; Pseudoparamonotonicity; 65 K10; 65 K15; 90 C25; 90 C33 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-017-1176-2

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