数学物理学报(英文版) ›› 2005, Vol. 25 ›› Issue (2): 359-366.

• 论文 • 上一篇    下一篇

GLOBAL WEAK SHARP MINIMA AND COMPLETENESS OF METRIC SPACE

黄辉   

  1. Department of Mathematics, Zhongshan University, Guangzhou 510275, China
    Department of Mathematics, Yunnan University, Kunming 650091, China
  • 出版日期:2005-04-20 发布日期:2005-04-20
  • 基金资助:

    The research was supported by the National Natural
    Science Foundation of China(10361008) and the Natural Science Foundation of Yunnan Province(2003A002M).

GLOBAL WEAK SHARP MINIMA AND COMPLETENESS OF METRIC SPACE

 HUANG Hui   

  • Online:2005-04-20 Published:2005-04-20
  • Supported by:

    The research was supported by the National Natural
    Science Foundation of China(10361008) and the Natural Science Foundation of Yunnan Province(2003A002M).

摘要:

A sufficient condition on the existence of a global weak sharp minima for
general function in metric space is established. A characterization for convex function
to have global weak sharp minima is also presented, which generalized Burke and Ferris’
result[1] to infinite dimensional space. A characterization of the completeness of a metric
space is given by the existence of global weak sharp minima.

Abstract:

A sufficient condition on the existence of a global weak sharp minima for
general function in metric space is established. A characterization for convex function
to have global weak sharp minima is also presented, which generalized Burke and Ferris’
result[1] to infinite dimensional space. A characterization of the completeness of a metric
space is given by the existence of global weak sharp minima.

Key words: Global weak sharp minima;completeness;convex function

中图分类号: 

  • 90C31