Non polyhedral convex envelopes for 1-convex functions

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• 作者：Marco Locatelli
• 刊名：Journal of Global Optimization
• 出版年：2016
• 出版时间：August 2016
• 年：2016
• 卷：65
• 期：4
• 页码：637-655
• 全文大小：519 KB
• 刊物类别：Business and Economics
• 刊物主题：Economics
  Operation Research and Decision Theory
  Computer Science, general
  Real Functions
  Optimization
  
• 出版者：Springer Netherlands
• ISSN：1573-2916
• 卷排序：65

文摘

In this paper we discuss how to derive the non polyhedral convex envelopes for some functions, called 1-convex throughout the paper, over boxes. The main result is about n-dimensional 1-convex functions, but we get to it by first discussing in detail some special cases, namely functions \(xyz^\delta \), \(\delta >1\), and, next, more general trivariate functions. The relation between the class of functions investigated in this paper and other classes investigated in the existing literature is discussed.KeywordsNon polyhedral convex envelopesTrivariate functions 1-Convex functions