Details

Autor(en) / Beteiligte

• Ceng, Lu-Chuan
• Köbis, Elisabeth
• Zhao, Xiaopeng

Titel

On general implicit hybrid iteration method for triple hierarchical variational inequalities with hierarchical variational inequality constraints

Ist Teil von

• Optimization, 2020-09, Vol.69 (9), p.1961-1986

Ort / Verlag

Philadelphia: Taylor & Francis

Erscheinungsjahr

2020

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• In this paper, we study the triple hierarchical variational inequality problem (THVIP, for short) with the hierarchical variational inequality constraint for finitely many nonexpansive mappings and an asymptotically nonexpansive mapping in a real Hilbert space. Based on Korpelevich's extragradient method, hybrid steepest-descent method, Mann's implicit iteration method and Halpern's iteration method, a general implicit hybrid iterative algorithm for solving this THVIP is proposed. Under mild conditions, the strong convergence of the iterative sequences generated by the algorithm is established. Our results improve and extend the corresponding results in the earlier and recent literature.