IJPAM: Volume 64, No. 4 (2010)

GENERALIZED RELATIVELY RELAXED PROXIMAL
POINT ALGORITHMS AND NONLINEAR
VARIATIONAL INCLUSION PROBLEMS

Ram U. Verma
Department of Mathematics
Texas A&M University
Kingsville, Texas, 78363, USA
e-mail: [email protected]


Abstract.Based on the notion of relatively maximal monotonicity, the approximation solvability of a general class of variational inclusion problems is investigated, while generalizing results of Xu (2002) on strong convergence using a modified proximal point algorithm, of Rockafellar (1976) on weak as well as strong convergence using the proximal point algorithm, and of Eckstein and Bertsekas (1992) on weak convergence applying the relaxed proximal point algorithms in a real Hilbert space setting. The obtained results generalize and unify most of the existing results on linear convergence to the context of relaxed/generalized proximal point algorithms in literature. Furthermore, they can also, in turn, be applied to first-order evolution equations as well as evolution inclusions.

Received: October 19, 2010

AMS Subject Classification: 49J40, 47H10, 65B05

Key Words and Phrases: inclusion problems, maximal monotone mapping, relatively maximal monotone mapping, generalized resolvent operator

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 64
Issue: 4