Novel self-adaptive algorithms for non-Lipschitz equilibrium problems with applications

Pham Ky Anh () and Trinh Ngoc Hai ()
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Pham Ky Anh: Vietnam National University
Trinh Ngoc Hai: Hanoi University of Science and Technology

Journal of Global Optimization, 2019, vol. 73, issue 3, No 9, 637-657

Abstract: Abstract In this paper, we introduce two self-adaptive algorithms for solving a class of non-Lipschitz equilibrium problems. These algorithms are very simple in the sense that at each step, they require only one projection onto a feasible set. Their convergence can be established under quite mild assumptions. More precisely, the weak (strong) convergence of the first algorithm is proved under the pseudo-paramonotonicity (strong pseudomonotonicity) conditions, respectively. Especially, the convexity in the second argument of the involving bifunction is not required. In the second algorithm, the weak convergence is established under the pseudomonotonicity. Moreover, it is proved that under some additional conditions, the solvability of the equilibrium problem is equivalent to the boundedness of the sequences generated by the proposed algorithms. Some applications to the optimization problems and variational inequality problems as well as to transport equilibrium problems are also considered.

Keywords: Equilibrium problem; Variational inequality; Fixed point problem; Solution existence; Non-convex optimization; Self-adaptive algorithm; 47H05; 47J25; 65K10; 90C25; 90C33 (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/s10898-018-0722-2

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