Asymptotic Convergence Analysis of The Proximal Point Algorithm for Metrically Regular Mappings
5th International Workshop on Computational Intelligence & Applications Proceedings : IWCIA 2009
Page 270-273
published_at 2009-11
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Title ( eng ) |
Asymptotic Convergence Analysis of The Proximal Point Algorithm for Metrically Regular Mappings
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Creator |
Matsushita Shin-ya
Xu Li
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Source Title |
5th International Workshop on Computational Intelligence & Applications Proceedings : IWCIA 2009
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Start Page | 270 |
End Page | 273 |
Abstract |
This paper studies convergence properties of the proximal point algorithm when applied to a certain class of nonmonotone set-valued mappings. We consider an algorithm for solving an inclusion 0 ∈ T(x), where T is a metrically regular set-valued mapping acting from Rn into Rm. The algorithm is given by the follwoing iteration: x0 ∈ Rn and
xk+1 = αkxk + (1 - αk)yk, for k = 0, 1, 2, . . ., where {αk} is a sequence in [0, 1] such that αk ≤ ¯α < 1, gk is a Lipschitz mapping from Rn into Rm and yk satisfies the following inclusion 0 ∈ gk(yk) - gk(xk) + T(yk). We prove that if the modulus of regularity of T is sufficiently small then the sequence generated by our algorithm converges to a solution to 0 ∈ T(x). |
NDC |
Technology. Engineering [ 500 ]
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Language |
eng
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Resource Type | conference paper |
Publisher |
IEEE SMC Hiroshima Chapter
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Date of Issued | 2009-11 |
Rights |
(c) Copyright by IEEE SMC Hiroshima Chapter.
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Publish Type | Version of Record |
Access Rights | open access |
Source Identifier |
[ISSN] 1883-3977
[URI] http://www.hil.hiroshima-u.ac.jp/iwcia/2009/
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