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Line 55: These classical subgradient methods have poor performance and are no longer recommended for general use. ==Subgradient-projection methods== During the 1970s, [[Claude Lemaréchal]] and [[Phil. Wolfe]] ~~developed~~proposed "bundle methods" of descent for problems of convex minimization. These bundle methods are related to the subgradient projection methods of [[Boris T. Polyak]] (~~1966~~1969).<ref> {{cite book \| last = Bertsekas Line 67: \| isbn = 1-886529-00-0 }} </ref> On some problems, subgradient-projection methods are surprisingly competitive with proximal-bundle methods of descent; both subgradient-projection methods and contemporary bundle-methods often use "ballstep" rules for choosing step-sizes.<~~ref>[[Claude Lemaréchal]] "Lagrangian Relaxation", ''Combinatorial Optimization'', ''Lecture Notes in Computer Science'', Springer Verlag.</~~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\|id={{MR\|1900016}}.{{doi\|10.1007/3-540-45586-8_4}}\|}} </ref> ==Constrained optimization==

Subgradient method: Difference between revisions