A necessary and sufficient criterion for the existence of the global minima of a continuous lower bounded function on a noncompact set

摘要

In this paper, we provide a necessary and sufficient criterion for the existence of the global minima of a continuous lower bounded function defined on a noncompact set. Our criterion is based on a new existence level introduced in this paper that describes the behavior of the function as its argument approaches the extended boundary of the minimization domain. Some examples are included to illustrate the efficiency of our criterion. (C) 2020 Elsevier B.V. All rights reserved.