NDLI: Lagrange Duality in Set Optimization

Content Provider	Springer Nature Link
Author	Hamel, Andreas H. Löhne, Andreas
Copyright Year	2013
Abstract	Based on the complete-lattice approach, a new Lagrangian type duality theory for set-valued optimization problems is presented. In contrast to previous approaches, set-valued versions for the known scalar formulas involving infimum and supremum are obtained. In particular, a strong duality theorem, which includes the existence of the dual solution, is given under very weak assumptions: The ordering cone may have an empty interior or may not be pointed. “Saddle sets” replace the usual notion of saddle points for the Lagrangian, and this concept is proven to be sufficient to show the equivalence between the existence of primal/dual solutions and strong duality on the one hand, and the existence of a saddle set for the Lagrangian on the other hand. Applications to set-valued risk measures are indicated.
Starting Page	368
Ending Page	397
Page Count	30
File Format	PDF
ISSN	00223239
Journal	Journal of Optimization Theory and Applications
Volume Number	161
Issue Number	2
e-ISSN	15732878
Language	English
Publisher	Springer US
Publisher Date	2013-10-01
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Set optimization Lagrangian Set relation Convex duality Complete lattice Saddle points Risk measures Calculus of Variations and Optimal Control; Optimization Optimization Theory of Computation Applications of Mathematics Engineering Operations Research/Decision Theory
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Control and Optimization Management Science and Operations Research

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