Accelerated projection methods for quasimonotone bilevel variational inequality problems with applications

In this paper, we propose two novel alternated multi-step inertial projection algorithms with self-adaptive step sizes. These algorithms are employed to solve the quasimonotone bilevel variational inequality problem (QBVIP, where VIP denotes a variational inequality problem) with a variational inclu...

Celý popis

Uložené v:
Podrobná bibliografia
Vydané v:Communications in nonlinear science & numerical simulation Ročník 150; s. 108988
Hlavní autori: Wang, Meiying, Liu, Hongwei, Yang, Jun, Wei, Xinyi
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Elsevier B.V 01.11.2025
Predmet:
Alternated multi-step inertia
Bilevel variational inequality
Projection method
Quasimonotone mapping
Projection method
Bilevel variational inequality
47J20
90C25
Quasimonotone mapping
Alternated multi-step inertia
47H05
47J25
ISSN:1007-5704
On-line prístup:Získať plný text
Tagy: Pridať tag
Žiadne tagy, Buďte prvý, kto otaguje tento záznam!
Popis
Shrnutí:In this paper, we propose two novel alternated multi-step inertial projection algorithms with self-adaptive step sizes. These algorithms are employed to solve the quasimonotone bilevel variational inequality problem (QBVIP, where VIP denotes a variational inequality problem) with a variational inclusion constraint in a real Hilbert space, where the QBVIP involves a strongly monotone mapping at the upper-level VIP and quasimonotone mapping at the lower-level. We establish the strong convergence of the proposed algorithms under some suitable conditions. Furthermore, we demonstrate the applicability of these algorithms to the split feasibility problem and the generalized Nash equilibrium problem. These works extend and develop some of the existing results in the literature. Finally, we apply our results to LASSO problem and numerical experiments demonstrate the effectiveness and superiority of the proposed algorithms. •This paper studies bilevel variational inequality problems with a quasimonotone operator.•The algorithms use alternating multi-step inertia terms to improve convergence.•No prior knowledge of the Lipschitz constant and strong monotonicity is required.•The sequentially weakly continuity of A is replaced by a weaker condition.
ISSN:1007-5704
DOI:10.1016/j.cnsns.2025.108988