ISSN:
1573-2878
Keywords:
Augmented penalty function
;
duality theory
;
generalized Lagrangian function
;
method of multipliers
;
nonconvex programming
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract As is well known, a saddle point for the Lagrangian function, if it exists, provides a solution to a convex programming problem; then, the values of the optimal primal and dual objective functions are equal. However, these results are not valid for nonconvex problems. In this paper, several results are presented on the theory of the generalized Lagrangian function, extended from the classical Lagrangian and the generalized duality program. Theoretical results for convex problems also hold for nonconvex problems by extension of the Lagrangian function. The concept of supporting hypersurfaces is useful to add a geometric interpretation to computational algorithms. This provides a basis to develop a new algorithm.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00933876
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