Comparison of two approximal proximal point algorithms for monotone variational inequalities

O221.2; Proximal point algorithms (PPA) are attractive methods for solving monotone variational inequalities (MVI). Since solving the sub-problem exactly in each iteration is costly or sometimes impossible, various approximate versions ofPPA (APPA)are developed for practical applications. In this pa...

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Published in:Journal of Zhejiang University. A. Science Vol. 8; no. 6; pp. 969 - 977
Main Author: Tao, Min
Format: Journal Article
Language:English
Published: School of Applied Mathematics and Physics, Nanjing University of Posts and Telecommunications, Nanjing 210003, China 01.05.2007
Subjects:
Projection and contraction methods
Proximal point algorithm (PPA)
Prediction and correction
Monotone varia tional inequality (MVI)
Approximate PPA (APPA)
ISSN:1673-565X, 1862-1775
Online Access:Get full text
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Abstract O221.2; Proximal point algorithms (PPA) are attractive methods for solving monotone variational inequalities (MVI). Since solving the sub-problem exactly in each iteration is costly or sometimes impossible, various approximate versions ofPPA (APPA)are developed for practical applications. In this paper, we compare two APPA methods, both of which can be viewed as prediction-correction methods. The only difference is that they use different search directions in the correction-step. By extending the general forward-backward splitting methods, we obtain Algorithm Ⅰ; in the same way, Algorithm Ⅱ is proposed by spreading the general extra-gradient methods. Our analysis explains theoretically why Algorithm Ⅱ usually outperforms Algorithm Ⅰ.For computation practice, we consider a class of MVI with a special structure, and choose the extending Algorithm Ⅱ to implement, which is inspired by the idea of Gauss-Seidel iteration method making full use of information about the latest iteration.And in particular, self-adaptive techniques are adopted to adjust relevant parameters for faster convergence. Finally, some numerical experiments are reported on the separated MVI. Numerical results showed that the extending Algorithm Ⅱ is feasible and easy to implement with relatively low computation load.
AbstractList O221.2; Proximal point algorithms (PPA) are attractive methods for solving monotone variational inequalities (MVI). Since solving the sub-problem exactly in each iteration is costly or sometimes impossible, various approximate versions ofPPA (APPA)are developed for practical applications. In this paper, we compare two APPA methods, both of which can be viewed as prediction-correction methods. The only difference is that they use different search directions in the correction-step. By extending the general forward-backward splitting methods, we obtain Algorithm Ⅰ; in the same way, Algorithm Ⅱ is proposed by spreading the general extra-gradient methods. Our analysis explains theoretically why Algorithm Ⅱ usually outperforms Algorithm Ⅰ.For computation practice, we consider a class of MVI with a special structure, and choose the extending Algorithm Ⅱ to implement, which is inspired by the idea of Gauss-Seidel iteration method making full use of information about the latest iteration.And in particular, self-adaptive techniques are adopted to adjust relevant parameters for faster convergence. Finally, some numerical experiments are reported on the separated MVI. Numerical results showed that the extending Algorithm Ⅱ is feasible and easy to implement with relatively low computation load.
Author Tao, Min
AuthorAffiliation School of Applied Mathematics and Physics, Nanjing University of Posts and Telecommunications, Nanjing 210003, China
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10.1007/BF01582255
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Keywords Projection and contraction methods
Proximal point algorithm (PPA)
Prediction and correction
Monotone varia tional inequality (MVI)
Approximate PPA (APPA)
Language English
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References C.L. Li (969_CR5) 2003; 25
G.M. Korpelevich (969_CR4) 1976; 12
R.T. Rockafellar (969_CR6) 1976; 14
P. Tseng (969_CR7) 2000; 38
B.S. He (969_CR3) 2004
T. Zhu (969_CR8) 2004; 7
P.T. Harker (969_CR2) 1990; 48
D.P. Bertsekas (969_CR1) 1989
References_xml – volume: 38
  start-page: 431
  year: 2000
  ident: 969_CR7
  publication-title: SIAM J. Control & Optim.
  doi: 10.1137/S0363012998338806
– volume: 48
  start-page: 161
  year: 1990
  ident: 969_CR2
  publication-title: Math. Programming
  doi: 10.1007/BF01582255
– volume: 12
  start-page: 747
  year: 1976
  ident: 969_CR4
  publication-title: Ekonomika i Matematchskie Metody
– start-page: 267
  volume-title: Parallel and Distributed Computation, Numerical Methods
  year: 1989
  ident: 969_CR1
– volume: 7
  start-page: 453
  year: 2004
  ident: 969_CR8
  publication-title: Math. Ineq. Appl.
– volume: 25
  start-page: 269
  year: 2003
  ident: 969_CR5
  publication-title: Num. Comput. Appl. Computer
– start-page: 15
  volume-title: Numerical Linear Algebra and Optimization. Proc. 2003 Int. Conf. Numerical Optimization and Numerical Linear Algebra
  year: 2004
  ident: 969_CR3
– volume: 14
  start-page: 877
  year: 1976
  ident: 969_CR6
  publication-title: SIAM J. Control & Optim.
  doi: 10.1137/0314056
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Snippet O221.2; Proximal point algorithms (PPA) are attractive methods for solving monotone variational inequalities (MVI). Since solving the sub-problem exactly in...
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Title Comparison of two approximal proximal point algorithms for monotone variational inequalities
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