Algorithms for nonlinear constraints that use lagrangian functions

by: MJD Powell

Mathematical Programming, Vol. 14, No. 1. (1 December 1978), pp. 224-248.

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Abstract

Lagrangian functions are the basis of many of the more successful methods for nonlinear constraints in optimization calculations. Sometimes they are used in conjunction with linear approximations to the constraints and sometimes penalty terms are included to allow the use of algorithms for unconstrained optimization. Much has been discovered about these techniques during the last eight years and this paper gives a view of the progress and understanding that has been achieved and its relevance to practical algorithms. A particular method is recommended that seems to be more powerful than the author believed to be possible at the beginning of 1976.

@article{citeulike:2790820, abstract = {Lagrangian functions are the basis of many of the more successful methods for nonlinear constraints in optimization calculations. Sometimes they are used in conjunction with linear approximations to the constraints and sometimes penalty terms are included to allow the use of algorithms for unconstrained optimization. Much has been discovered about these techniques during the last eight years and this paper gives a view of the progress and understanding that has been achieved and its relevance to practical algorithms. A particular method is recommended that seems to be more powerful than the author believed to be possible at the beginning of 1976.}, author = {Powell, M. J. D. }, citeulike-article-id = {2790820}, doi = {10.1007/BF01588967}, journal = {Mathematical Programming}, keywords = {optimization, quasi-newton-methods}, month = {December}, number = {1}, pages = {224--248}, posted-at = {2008-05-12 21:54:33}, priority = {2}, title = {Algorithms for nonlinear constraints that use lagrangian functions}, url = {http://dx.doi.org/10.1007/BF01588967}, volume = {14}, year = {1978} }

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TY - JOUR ID - citeulike:2790820 L3 - citeulike-article-id:2790820 TI - Algorithms for nonlinear constraints that use lagrangian functions JF - Mathematical Programming VL - 14 IS - 1 SP - 224 EP - 248 N2 - Lagrangian functions are the basis of many of the more successful methods for nonlinear constraints in optimization calculations. Sometimes they are used in conjunction with linear approximations to the constraints and sometimes penalty terms are included to allow the use of algorithms for unconstrained optimization. Much has been discovered about these techniques during the last eight years and this paper gives a view of the progress and understanding that has been achieved and its relevance to practical algorithms. A particular method is recommended that seems to be more powerful than the author believed to be possible at the beginning of 1976. KW - optimization KW - quasi-newton-methods AU - Powell, MJD PY - 1978/12/01/ UR - http://dx.doi.org/10.1007/BF01588967 ER -

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