ON THE CONVEXITY OF PIECEWISE-DEFINED FUNCTIONS

被引：9
|
作者：
Bauschke, Heinz H. [1 ]
Lucet, Yves [2 ]
Phan, Hung M. [3 ]
机构：
[1] Univ British Columbia Okanagan, Math, Kelowna, BC V1V 1V7, Canada
[2] Univ British Columbia Okanagan, Comp Sci, Kelowna, BC V1V 1V7, Canada
[3] Univ Massachusetts Lowell, Dept Math Sci, Lowell, MA 01854 USA
来源：
ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS | 2016年 / 22卷 / 03期
基金：
加拿大自然科学与工程研究理事会;
关键词：
Computer-aided convex analysis; convex function; convex interpolation; convex set; piecewise-defined function; CONJUGATE;
D O I：
10.1051/cocv/2015023
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
Functions that are piecewise defined are a common sight in mathematics while convexity is a property especially desired in optimization. Suppose now a piecewise-defined function is convex on each of its defining components - when can we conclude that the entire function is convex? In this paper we provide several convenient, verifiable conditions guaranteeing convexity (or the lack thereof). Several examples are presented to illustrate our results.
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页码：728 / 742
页数：15
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