A Decomposition Algorithm for Convex Nondifferentiable Minimization with Errors

作者: Yuan Lu , Li-Ping Pang , Jie Shen , Xi-Jun Liang

DOI: 10.1155/2012/215160

关键词:

摘要: A decomposition algorithm based on proximal bundle-type method with inexact data is presented for minimizing an unconstrained nonsmooth convex function . At each iteration, only the approximate evaluation of and its subgradients are required which make easier to implement. It shown that every cluster sequence iterates generated by proposed exact solution minimization problem. Numerical tests emphasize theoretical findings.

参考文章(12)
Robert Mifflin, Claudia Sagastizábal, VU-Decomposition Derivatives for Convex Max-Functions Lecture Notes in Economics and Mathematical Systems. pp. 167- 186 ,(1999) , 10.1007/978-3-642-45780-7_11
Jardim Bot, Estrada Dona Castorina, Claudia SagastizÊabal, Robert Mi, Proximal Points are on the Fast Track ,(2002)
Michael Hintermüller, A Proximal Bundle Method Based on Approximate Subgradients Computational Optimization and Applications. ,vol. 20, pp. 245- 266 ,(2001) , 10.1023/A:1011259017643
Claude Lemaréchal, François Oustry, Claudia Sagastizábal, The -Lagrangian of a convex function Transactions of the American Mathematical Society. ,vol. 352, pp. 711- 729 ,(1999) , 10.1090/S0002-9947-99-02243-6
J.J. Moreau, Proximité et dualité dans un espace hilbertien Bulletin de la Société mathématique de France. ,vol. 79, pp. 273- 299 ,(1965) , 10.24033/BSMF.1625
Yuan Lu, Li-Ping Pang, Xi-Jun Liang, Zun-Quan Xia, An approximate decomposition algorithm for convex minimization Journal of Computational and Applied Mathematics. ,vol. 234, pp. 658- 666 ,(2010) , 10.1016/J.CAM.2010.01.003
Robert Mifflin, Claudia Sagastizábal, On $\mathcalVU$-theory for Functions with Primal-Dual Gradient Structure Siam Journal on Optimization. ,vol. 11, pp. 547- 571 ,(2000) , 10.1137/S1052623499350967
R. Tyrrell Rockafellar, Monotone Operators and the Proximal Point Algorithm SIAM Journal on Control and Optimization. ,vol. 14, pp. 877- 898 ,(1976) , 10.1137/0314056
Rafael Correa, Claude Lemaréchal, Convergence of some algorithms for convex minimization Mathematical Programming. ,vol. 62, pp. 261- 275 ,(1993) , 10.1007/BF01585170
Robert Mifflin, Claudia Sagastizábal, A **-algorithm for convex minimization Mathematical Programming. ,vol. 104, pp. 583- 608 ,(2005) , 10.1007/S10107-005-0630-3