arXiv subjects

Le Hai Yen

Publications and source records attributed to Le Hai Yen.

4 recordsLinked to original sources

arXiv2023

An extragradient algorithm for quasiconvex equilibrium problems without monotonicity

We attempt to provide an algorithm for approximating a solution of the quasiconvex equilibrium problem that was proved to exist by K. Fan 1972. The proposed algorithm is an iterative procedure, where the search direction at each iteration is a normal-subgradient, while the step-size is updated avoiding Lipschitz-type conditions. The algorithm is convergent to a $ρ$- quasi-solution with any positive $ρ$ if the bifunction $f$ is semistrictly quasiconvex in its second variable, while it converges to the solution when $f$ is strongly quasiconvex. Neither monotoniciy nor Lipschitz property is required.

math.OC↗

arXiv2020

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

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.

math.OC↗

arXiv2019

A subgradient method for equilibrium problems involving quasiconvex bifunctions

In this paper we propose a subgradient algorithm for solving the equilibrium problem where the bifunction may be quasiconvex with respect to the second variable. The convergence of the algorithm is investigated. A numerical example for a generalized variational inequality problem is provided to demonstrate the behavior of the algorithm.

math.OC↗

arXiv2012

High Energy Scattering in the Quasi-Potential Approach

Asymptotic behavior of the scattering amplitude for two scalar particles by scalar, vector and tensor exchanges at high energy and fixed momentum transfers is reconsidered in quantum field theory. In the framework of the quasi-potential approach and the modified perturbation theory a systematic scheme of finding the leading eikonal scattering amplitudes and its corrections are developed and constructed.The connection between the solutions obtained by quasi-potential and functional approaches is also discussed.The first correction to leading eikonal amplitude is found. Keywords: Eikonal scattering theory, Quantum gravity.

hep-th↗