Subgradient method: Difference between revisions

Revision as of 19:35, 21 April 2011

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</ref> Contemporary bundle-methods often use "[[level set|level]] control" rules for choosing step-sizes, developing techniques from the "subgradient-projection" method of Boris T. Polyak (1969). However, there are problems on which bundle methods offer little advantage over subgradient-projection methods.<ref>

{{cite book| last=Lemaréchal|first=Claude|authorlink=Claude Lemaréchal|chapter=Lagrangian relaxation|pages=112–156|url=http://dx.doi.org/10.1007/3-540-45586-8_4|title=Computational combinatorial optimization: Papers from the Spring School held in Schloß Dagstuhl, May 15–19, 2000|editor=Michael Jünger and Denis Naddef|series=Lecture Notes in Computer Science|volume=2241|publisher=Springer-Verlag| ___location=Berlin|year=2001|isbn=3-540-42877-1|mr=1900016|doi=10.1007/3-540-45586-8_4|ref=harv}}</ref><ref>

{{cite articlejournal|last1=Kiwiel|first1=Krzysztof&nbsp;C.|last2=Larsson |first2=Torbjörn|last3=Lindberg|first3=P.&nbsp;O.|title=Lagrangian relaxation via ballstep subgradient methods|url=http://mor.journal.informs.org/cgi/content/abstract/32/3/669 |journal=Mathematics of Operations Research|volume=32|year=2007|number=3|pages=669–686|month=August|MR=2348241|doi=10.1287/moor.1070.0261|ref=harv}}

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