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Constructing Generalized Mean Functions Using Convex Functions with Regularity Conditions

Y.B. ZHAO (ybzhao***at***amss.ac.cn)
S.C Fang (fang***at***eos.ncsu.edu)
D. Li (dli***at***se.cuhk.edu.hk)

Abstract: The generalized mean function has been widely used in convex analysis and mathematical programming. This paper studies a further generalization of such a function. A necessary and sufficient condition is obtained for the convexity of a generalized function. Additional sufficient conditions that can be easily checked are derived for the purpose of identifying some classes of functions which guarantee the convexity of the generalized functions. We show that some new classes of convex functions with certain regularity (such as $S^*$-regularity) can be used as building blocks to construct such generalized functions.

Keywords: Convexity, mathematical programming, generalized mean function, self-concordant functions, $S^*$-regular functions.

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )

Category 2: Convex and Nonsmooth Optimization (Generalized Convexity/Monoticity )

Category 3: Nonlinear Optimization


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Entry Submitted: 06/27/2005
Entry Accepted: 06/27/2005
Entry Last Modified: 06/27/2005

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