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→Basic subgradient update: Rewrite, correcting "algorithm" when "iterative method" is needed, etc. |
→Convergence results: >Claude Lemaréchal "Lagrangian Relaxation", ''Combinatorial Optimization'', ''Lecture Notes in Computer Science'', Springer Verlag. </ref> |
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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 bundle methods of descent for problems of convex minimization. These bundle methods are related to the subgradient projection methods of [[Boris Polyak]] (1966).<ref>
{{cite book
| last = Bertsekas
| first = Dimitri P.
| authorlink = Dimitri P. Bertsekas
| title = Nonlinear Programming
| edition = Second
| publisher = Athena Scientific
| date = 1999
| ___location = Cambridge, MA.
| 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>
==Constrained optimization==
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