BUNDLE METHODS IN THE XXIst CENTURY: A BIRD'S-EYE VIEW

作者: Welington de Oliveira , Claudia Sagastizábal

DOI: 10.1590/0101-7438.2014.034.03.0647

关键词:

摘要: Bundle methods are often the algorithms of choice for nonsmooth convex optimization, especially if accuracy in solution and reliability a concern. We review several based on bundle methodology that have been developed recently that, unlike their forerunner variants, ability to provide exact solutions even most time available information is inaccurate. adopt an approach by no means exhaustive, but covers different proximal level dealing with inexact oracles, both unconstrained constrained problems.

参考文章(43)
C. Lemarechal, An extension of davidon methods to non differentiable problems Nondifferentiable Optimization. pp. 95- 109 ,(1975) , 10.1007/BFB0120700
Michael Hintermüller, A Proximal Bundle Method Based on Approximate Subgradients Computational Optimization and Applications. ,vol. 20, pp. 245- 266 ,(2001) , 10.1023/A:1011259017643
Darinka Dentcheva, Alexander Shapiro, Andrzej P. Ruszczyński, Lectures on Stochastic Programming: Modeling and Theory ,(2009)
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
Robert Mifflin, An Algorithm for Constrained Optimization with Semismooth Functions Mathematics of Operations Research. ,vol. 2, pp. 191- 207 ,(1977) , 10.1287/MOOR.2.2.191
Peter Richtárik, Approximate Level Method for Nonsmooth Convex Minimization Journal of Optimization Theory and Applications. ,vol. 152, pp. 334- 350 ,(2012) , 10.1007/S10957-011-9908-1
Antonio Frangioni, Bernard Gendron, A Stabilized Structured Dantzig-Wolfe Decomposition Method Mathematical Programming. ,vol. 140, pp. 45- 76 ,(2013) , 10.1007/S10107-012-0626-8
C. Sagastizábal, Divide to conquer: decomposition methods for energy optimization Mathematical Programming. ,vol. 134, pp. 187- 222 ,(2012) , 10.1007/S10107-012-0570-7
Claude Lemaréchal, Claudia Sagastizábal, Variable metric bundle methods: from conceptual to implementable forms Mathematical Programming. ,vol. 76, pp. 393- 410 ,(1997) , 10.1007/BF02614390
Wim van Ackooij, Welington de Oliveira, Level bundle methods for constrained convex optimization with various oracles Computational Optimization and Applications. ,vol. 57, pp. 555- 597 ,(2014) , 10.1007/S10589-013-9610-3