ISSN:
1572-9281
Keywords:
vector optimization
;
positively proprer minima
;
augmented Lagrangian
;
Birkhoff orthogonality
;
quadratic growth condition
;
inf-stability
;
stability of degree 2
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract This paper shows how the use of penalty functions in terms of projections on the constraint cones, which are orthogonal in the sense of Birkhoff, permits to establish augmented Lagrangians and to define a dual problem of a given nonconvex vector optimization problem. Then the weak duality always holds. Using the quadratic growth condition together with the inf-stability or a kind of Rockafellar's stability called stability of degree two, we derive strong duality results between the properly efficient solutions of the two problems. A strict converse duality result is proved under an additional convexity assumption, which is shown to be essential.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1009753224825
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