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Title: Optimality for Set Functions with Values in Ordered Vector Spaces
Authors: H. C. Lai;L. J. Lin
Contributors: 數學系
Keywords: Convex set functions;strictly convex set functions;convex
subfamily of measurable subsets
;ordered vector spaces;normal cones;C-convex set functions;minimal points, weak minimal points;saddle
;weak saddle points;subdifferentials;weak subdifferentials;order-complete vector lattices
Date: 1989-12
Issue Date: 2011-05-10T06:44:55Z
Publisher: Springer Verlag
Abstract: Let (X, F,/z) be a finite atomless measure space, 5e a convex
subfamily of F, and Y and Z locally convex Hausdortt topological
vector spaces which are ordered by the cones C and D, respectively.
Let F:5�-~ Y be C-convex and G:oW~ Z be D-convex set functions.
Consider the following optimization problem (P): minimize F(f~), subject
to i2cff and G(l)) ---o 0. The paper generalizes the Moreau-
Rockafellar theorem with set functions. By applying this theorem, a
Kuhn-Tucker type optimality condition and a Fritz John type optimality
condition for problem (P) are established. The duality theorem for
problem (P) is also studied.
Relation: Journal of Optimization Theory and Applications, 63(3):371-389
Appears in Collections:[math] Periodical Articles

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