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Saddle point and duality in the optimization theory of convex set functions

Published online by Cambridge University Press:  17 February 2009

Hang-Chin Lai  and
Shu-Shih Yang
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Abstract

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For a set function G on an atomless finite measure space (X, , m), we define the subgradient, conjugate set of and conjugate functional of G. It is proved that a minimization problem of set function G has an optimal solution if and only if the Lagrangian on × L1(X, , m)has a saddle point (Ω0, f0) such that

where f0 is an element of the conjugate set (for the definition, see the later context).

Type
Research Article
Information
The ANZIAM Journal , Volume 24 , Issue 2 , October 1982 , pp. 130 - 137
Copyright
Copyright © Australian Mathematical Society 1982

References

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