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

Yen, Le Hai; Huyền, Nguyễn Thị Thanh; Mưu, Lê Dũng

doi:10.1007/s10898-018-00735-0

Cited by 20 publications

(2 citation statements)

References 31 publications

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“…Based upon the auxiliary problem principle, a lot numbers of algorithms using techniques of mathematical programming methods have been developed for solving problem (EP), e.g. [3,12,16,19,22,23,24,25] and the references therein, however to our best knowledges, all of them require that the bifunction f is convex with respect to its second variable. In our recent preprint [26] we developed an algorithm for problem (EP), where the bifunction f may be quasiconvex in its second variable.…”

Section: (Ep )mentioning

confidence: 99%

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A parallel subgradient projection algorithm for quasiconvex equilibrium problems under the intersection of convex sets

Yen¹,

Mưu²

2020

Preprint

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In this paper, we studied the equilibrium problem where the bi-function may be quasiconvex with respect to the second variable and the feasible set is the intersection of a finite number of convex sets. We propose a projection-algorithm, where the projection can be computed independently onto each component set. The convergence of the algorithm is investigated and numerical examples for a variational inequality problem involving affine fractional operator are provided to demonstrate the behavior of the algorithm.

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Section: (Ep )mentioning

confidence: 99%

“…The paramonotonicity of a bifunction is an extension of that for an operator, see e.g., [10], which has been used in some papers, see, for example, [1,22,25] (A3) The solution set S(EP ) is nonempty.…”

Section: A Parallel Algorithm and Its Convergencementioning

confidence: 99%