Robustness of the Hybrid Extragradient Proximal-Point Algorithm

作者: R. S. Burachik , S. Scheimberg , B. F. Svaiter

DOI: 10.1023/A:1017523331361

关键词:

摘要: The hybrid extragradient proximal-point method recently proposed by Solodov and Svaiter has the distinctive feature of allowing a relative error tolerance. We extend tolerance this method, proving that it converges even if summable is added to error. Furthermore, step may be performed inexactly with present convergence analysis, which encompasses other well-known variations previously unrelated. establish weak global under mild assumptions.

参考文章(28)
Regina S. Burachik, Claudia Sagastizábal, B. F. Svaiter, Bundle Methods for Maximal Monotone Operators Lecture Notes in Economics and Mathematical Systems. pp. 49- 64 ,(1999) , 10.1007/978-3-642-45780-7_4
Regina Sandra Burachik, B. F. Svaiter, ε-Enlargements of Maximal Monotone Operators in Banach Spaces Set-valued Analysis. ,vol. 7, pp. 117- 132 ,(1999) , 10.1023/A:1008730230603
Regina S. Burachik, Alfredo N. Iusem, B. F. Svaiter, Enlargement of Monotone Operators with Applications to Variational Inequalities Set-valued Analysis. ,vol. 5, pp. 159- 180 ,(1997) , 10.1023/A:1008615624787
Regina S. Burachik, Claudia A. Sagastizábal, B. F. Svaiter, ε-Enlargements of Maximal Monotone Operators: Theory and Applications Springer, Boston, MA. pp. 25- 43 ,(1998) , 10.1007/978-1-4757-6388-1_2
Bernard Lemaire, About the Convergence of the Proximal Method Lecture Notes in Economics and Mathematical Systems. pp. 39- 51 ,(1992) , 10.1007/978-3-642-51682-5_4
G. M. Korpelevich, The extragradient method for finding saddle points and other problems Matecon. ,vol. 12, pp. 747- 756 ,(1976)
Stephen M. Robinson, Generalized equations and their solutions, Part I: Basic theory Mathematical Programming Studies. pp. 128- 141 ,(1979) , 10.1007/BFB0120850
Boris T Poljak, Introduction to optimization Optimization Software, Publications Division. ,(1987)
H. Brézis, Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert North-Holland Pub. Co , American Elsevier Pub. Co.. ,(1973)