Auxiliary problems and algorithm for a system of generalized variational-like inequality problems

• Published in: Applied mathematics and computation Vol. 187; no. 2; pp. 789 - 796
• Main Authors: Kazmi, K.R., Khan, F.A.
• Format: Journal Article
• Language: English
• Published: New York, NY Elsevier Inc 15.04.2007; Elsevier
• Subjects: Algorithm; Auxiliary problems; Calculus of variations and optimal control; Exact sciences and technology; Global analysis, analysis on manifolds; Mathematical analysis; Mathematics; Numerical analysis; Numerical analysis. Scientific computation; Partial differential equations; Sciences and techniques of general use; System of generalized variational-like inequalities; Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds; System of generalized variational-like inequalities; Algorithm; Auxiliary problems; Variational problem; Numerical analysis; Existence theorem; Existence of solution; Variational inequality; Applied mathematics; Hilbert problem; Algorithm analysis; System
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2006.08.157

In this paper, we consider a system of generalized variational-like inequality problems (SGVLIP) involving nondifferentiable terms, and its related auxiliary problems in real Hilbert spaces. An existence theorem for auxiliary problems is established. Further, by exploiting this theorem, an algorithm for the SGVLIP is constructed. Furthermore, we prove the existence of a unique solution of SGVLIP and discuss the convergence analysis of the algorithm. The technique and results presented in this paper generalize and unify the corresponding techniques and results given in [M.A. Noor, General nonlinear variational inequalities, J. Math. Anal. Appl. 126 (1987) 78–84; M.A. Noor, General variational inequalities, Appl. Math. Lett. 1 (1988) 119–122; M.A. Noor, Mixed variational-like inequalities, Commun. Appl. Nonlinear Anal. 1 (4) (1994) 63–75].