On inertial subgradient extragradient rule for monotone bilevel equilibrium problems
Lu-Chuan Ceng, Adrian Petruşel, Xiaolong Qin, Jen-Chih Yao
Abstract
In a real Hilbert space, let the GSVI and CFPP represent a general system of variational inclusions and a common fixed point problem of countable nonexpansive mappings and an asymptotically nonexpansive mapping, respectively.In this paper, via a new inertial subgradient extragradient rule we introduce and analyze two iterative algorithms for solving the monotone bilevel equilibrium problem (MBEP) with the GSVI and CFPP as constraints.Some strong convergence theorems for the proposed algorithms are established under some mild assumptions.Our results improve and extend some corresponding results in the earlier and very recent literature.
Topics & Concepts
Subgradient methodMathematicsHilbert spaceMonotone polygonCountable setConvergence (economics)Inertial frame of referenceApplied mathematicsFixed pointVariational inequalityWeak convergenceMathematical optimizationPure mathematicsMathematical analysisComputer scienceComputer securityAsset (computer security)Economic growthGeometryEconomicsQuantum mechanicsPhysicsOptimization and Variational AnalysisAdvanced Optimization Algorithms ResearchFixed Point Theorems Analysis