Role of Relative A-Maximal Monotonicity in Overrelaxed Proximal-Point Algorithms with Applications

R. P. Agarwal and R. U. Verma ()
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R. P. Agarwal: Florida Institute of Technology
R. U. Verma: International Publications

Journal of Optimization Theory and Applications, 2009, vol. 143, issue 1, No 1, 15 pages

Abstract: Abstract A general framework for a class of overrelaxed proximal point algorithms based on the notion of relative A-maximal monotonicity is introduced; then, the convergence analysis for solving a general class of nonlinear variational inclusion problems is explored. The framework developed in this communication is quite suitable, unlike other existing notions of generalized maximal monotonicity, including A-maximal (m)-relaxed monotonicity in literature, to generalize first-order nonlinear evolution equations/evolution inclusions based on the generalized nonlinear Yosida approximations in Hilbert spaces as well as in Banach spaces.

Keywords: Variational inclusions; Maximal monotone mapping; Relative A-maximal monotone mapping; Generalized resolvent operator (search for similar items in EconPapers)
Date: 2009
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DOI: 10.1007/s10957-009-9554-z

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