A dual approach to solving nonlinear programming problems by unconstrained optimization
 R. Tyrrell Rockafellar
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Several recent algorithms for solving nonlinear programming problems with equality constraints have made use of an augmented “penalty” Lagrangian function, where terms involving squares of the constraint functions are added to the ordinary Lagrangian. In this paper, the corresponding penalty Lagrangian for problems with inequality constraints is described, and its relationship with the theory of duality is examined. In the convex case, the modified dual problem consists of maximizing a differentiable concave function (indirectly defined) subject to no constraints at all. It is shown that any maximizing sequence for the dual can be made to yield, in a general way, an asymptotically minimizing sequence for the primal which typically converges at least as rapidly.
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 Title
 A dual approach to solving nonlinear programming problems by unconstrained optimization
 Journal

Mathematical Programming
Volume 5, Issue 1 , pp 354373
 Cover Date
 19731201
 DOI
 10.1007/BF01580138
 Print ISSN
 00255610
 Online ISSN
 14364646
 Publisher
 SpringerVerlag
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 Authors

 R. Tyrrell Rockafellar ^{(1)}
 Author Affiliations

 1. University of Washington, Seattle, Washington, USA