数学物理学报(英文版) ›› 2020, Vol. 40 ›› Issue (6): 1849-1873.doi: 10.1007/s10473-020-0615-6

• 论文 • 上一篇    下一篇

GLOBAL OPTIMIZATION OF THE DIFFERENCE OF TWO INCREASING PLUS-CONVEX-ALONG-RAYS FUNCTIONS

H. SHAHRIARIPOUR1, H. MOHEBI2   

  1. 1. Department of Mathematics, Graduate University of Advanced Technology, Kerman, Iran;
    2. Department of Mathematics and Mahani Mathematical Research Center, Shahid Bahonar University of Kerman, P. O. Box:76169133, Postal Code:7616914111, Kerman, Iran
  • 收稿日期:2019-06-06 修回日期:2020-07-17 出版日期:2020-12-25 发布日期:2020-12-30
  • 通讯作者: H. MOHEBI,E-mail:hmohebi@uk.ac.ir E-mail:hmohebi@uk.ac.ir
  • 作者简介:H. SHAHRIARIPOUR,E-mail:hakimeh-shahriari@yahoo.com
  • 基金资助:
    The second author was partially supported by the Mahani Mathematical Research Center, Iran, grant no:97/3267.

GLOBAL OPTIMIZATION OF THE DIFFERENCE OF TWO INCREASING PLUS-CONVEX-ALONG-RAYS FUNCTIONS

H. SHAHRIARIPOUR1, H. MOHEBI2   

  1. 1. Department of Mathematics, Graduate University of Advanced Technology, Kerman, Iran;
    2. Department of Mathematics and Mahani Mathematical Research Center, Shahid Bahonar University of Kerman, P. O. Box:76169133, Postal Code:7616914111, Kerman, Iran
  • Received:2019-06-06 Revised:2020-07-17 Online:2020-12-25 Published:2020-12-30
  • Contact: H. MOHEBI,E-mail:hmohebi@uk.ac.ir E-mail:hmohebi@uk.ac.ir
  • Supported by:
    The second author was partially supported by the Mahani Mathematical Research Center, Iran, grant no:97/3267.

摘要: The theory of increasing and convex-along-rays (ICAR) functions defined on a convex cone in a real locally convex topological vector space X was already well developed. In this paper, we first examine abstract convexity of increasing plus-convex-along-rays (IPCAR) functions defined on a real normed linear space X. We also study, for this class of functions, some concepts of abstract convexity, such as support sets and subdifferentials. Finally, as an application, we characterize the maximal elements of the support set of strictly IPCAR functions and give optimality conditions for the global minimum of the difference between two IPCAR functions.

关键词: increasing plus-convex-along-rays function, support set, maximal element, global minimum, DC-function

Abstract: The theory of increasing and convex-along-rays (ICAR) functions defined on a convex cone in a real locally convex topological vector space X was already well developed. In this paper, we first examine abstract convexity of increasing plus-convex-along-rays (IPCAR) functions defined on a real normed linear space X. We also study, for this class of functions, some concepts of abstract convexity, such as support sets and subdifferentials. Finally, as an application, we characterize the maximal elements of the support set of strictly IPCAR functions and give optimality conditions for the global minimum of the difference between two IPCAR functions.

Key words: increasing plus-convex-along-rays function, support set, maximal element, global minimum, DC-function

中图分类号: 

  • 90C46