OPTIMIZATION FOR PRODUCTS OF CONCAVE FUNCTIONS

被引：4

作者：

Kantrowitz, Robert ^{[1
]}

Neumann, Michael M. ^{[2
]}

机构：

[1] Hamilton Coll, Dept Math, Clinton, NY 13323 USA

[2] Mississippi State Univ, Dept Math & Stat, Mississippi State, MS 39762 USA

来源：

RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO | 2005年 / 54卷 / 02期

关键词：

Concave function; optimization; Gateaux derivative;

D O I：

10.1007/BF02874642

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

If h denotes the product of finitely many concave non-negative functions on a compact interval [a, b], then it is shown that there exist points alpha and beta with a <= alpha <= beta <= b such that h is strictly increasing on [alpha, alpha), constant on (alpha, beta), and strictly decreasing on (beta, b]. This structure theorem leads to an extension of several classical optimization results for concave functions on convex sets to the case of products of concave functions.

引用

页码：291 / 302

页数：12

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