GLOBAL WEAK SHARP MINIMA AND COMPLETENESS OF METRIC SPACE

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.