Relatively Inexact Proximal Point Algorithm and Linear Convergence Analysis | Zendy

Ram U. Verma | Zendy

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Relatively Inexact Proximal Point Algorithm and Linear Convergence Analysis

Author(s) -

Ram U. Verma

Publication year - 2009

Publication title -

international journal of mathematics and mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.21

H-Index - 39

eISSN - 1687-0425

pISSN - 0161-1712

DOI - 10.1155/2009/691952

Subject(s) - mathematics , lipschitz continuity , hilbert space , monotonic function , convergence (economics) , modes of convergence (annotated index) , inverse , compact convergence , class (philosophy) , normal convergence , weak convergence , algorithm , discrete mathematics , mathematical analysis , rate of convergence , isolated point , topological space , topological vector space , computer science , geometry , artificial intelligence , channel (broadcasting) , computer security , economics , asset (computer security) , economic growth , computer network

Based on a notion of relatively maximal (m)-relaxed monotonicity, the approximation solvability of a general class of inclusion problems is discussed, while generalizing Rockafellar's theorem (1976) on linear convergence using the proximal point algorithm in a real Hilbert space setting. Convergence analysis, based on this new model, is simpler and compact than that of the celebrated technique of Rockafellar in which the Lipschitz continuity at 0 of the inverse of the set-valued mapping is applied. Furthermore, it can be used to generalize the Yosida approximation, which, in turn, can be applied to first-order evolution equations as well as evolution inclusions

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