Acta mathematica scientia,Series B ›› 2005, Vol. 25 ›› Issue (2): 359-366.

• Articles • Previous Articles     Next Articles

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).

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

CLC Number: 

  • 90C31
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