National Changhua University of Education Institutional Repository : Item 987654321/8865
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题名: Moreau-Rockafellar Type Theorem for Convex Set Functions
作者: H. C. Lai;L. J. Lin
贡献者: 數學系
日期: 1988
上传时间: 2011-05-10T06:44:43Z
出版者: Academic Press Inc.
摘要: Let (X, Γ, μ) be an atomless finite measure space and Γ a convex subfamily. It is proved that the Moreau-Rockafellar theorem, ∂(F1 + ··· + Fn)(Ω) = ∂F1(Ω) + ··· + ∂Fn(Ω), holds for proper convex set functions F1, …, Fn and Ω ε if all set functions Fi, except possibly one, are w*-lower semicontinuous on . As applications, the Kuhn-Tucker type condition for an optimal solution of convex programming problem with set functions and the Fritz John type condition for an optimal solution of vector-valued minimization problem for set functions are obtained.
關聯: Journal of Mathematical Analysis and Applications, 132(2):558-571
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