NDLI: Convex Duality and Calculus: Reduction to Cones

Content Provider	Springer Nature Link
Author	Brinkhuis, J.
Copyright Year	2009
Abstract	An attempt is made to justify results from Convex Analysis by means of one method. Duality results, such as the Fenchel-Moreau theorem for convex functions, and formulas of convex calculus, such as the Moreau-Rockafellar formula for the subgradient of the sum of sublinear functions, are considered. All duality operators, all duality theorems, all standard binary operations, and all formulas of convex calculus are enumerated. The method consists of three automatic steps: first translation from the given setting to that of convex cones, then application of the standard operations and facts (the calculi) for convex cones, finally translation back to the original setting. The advantage is that the calculi are much simpler for convex cones than for other types of convex objects, such as convex sets, convex functions and sublinear functions. Exclusion of improper convex objects is not necessary, and recession directions are allowed as points of convex objects. The method can also be applied beyond the enumeration of the calculi.
Starting Page	439
Ending Page	453
Page Count	15
File Format	PDF
ISSN	00223239
Journal	Journal of Optimization Theory and Applications
Volume Number	143
Issue Number	3
e-ISSN	15732878
Language	English
Publisher	Springer US
Publisher Date	2009-05-22
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Convex analysis Duality Calculus Convex cones Binary operations Optimization Operations Research/Decision Theory Engineering Applications of Mathematics Theory of Computation Calculus of Variations and Optimal Control; Optimization
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Control and Optimization Management Science and Operations Research

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