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On the relationship between a continuous update method of multipliers and the generalized reduced gradient method
Author(s) -
Root R. R.,
Ragsdell K. M.
Publication year - 1980
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620151203
Subject(s) - penalty method , transformation (genetics) , mathematical optimization , mathematics , nonlinear programming , scheme (mathematics) , gradient method , sequence (biology) , dual (grammatical number) , function (biology) , nonlinear system , algorithm , continuous function (set theory) , computer science , mathematical analysis , art , biochemistry , chemistry , physics , genetics , literature , quantum mechanics , evolutionary biology , biology , gene
The method of multipliers 1–3 (MOM) is a transformation technique which has enjoyed considerable popularity in recent years. The algorithmic philosophy is similar to conventional penalty function methods in that a constrained nonlinear programming problem is transformed into a sequence of unconstrained problems. In the standard MOM approach, the multipliers are updated after each unconstrained search. In this paper we investigate methods which involve continuous updating of the penalty parameters and design variables. We demonstrate that this continuous updating scheme is equivalent to the generalized reduced gradient method 4,5 applied to a certain dual problem. Computational results are given which suggest that the continuous updating MOM is not as efficient as one might reasonably hope.