On Functions Whose Stationary Points Are Global Minima
STANFORD UNIV CA DEPT OF OPERATIONS RESEARCH
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In this paper a characterization of functions whose stationary points are global minima is studied. By considering the level sets of a real function as a point-to-set mapping, and by examining its semi-continuity properties, we obtain a result that a real function, defined on a subset of Rn and satisfying some mild regularity conditions, belongs to the above family if and only if the point-to-set mapping of its level sets is strictly lower semicontinuous. Mathematical programming applications are also mentioned.
- Operations Research