Abstract
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 semicontinuity properties, we obtain the result that a real function, defined on a subset of Rn and satisfying some mild regularity conditions, belongs to the above family iff the point-to-set mapping of its level sets is strictly lower semicontinuous. Mathematical programming applications are also mentioned.
Original language | English |
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Pages (from-to) | 195-208 |
Number of pages | 14 |
Journal | Journal of Optimization Theory and Applications |
Volume | 22 |
Issue number | 2 |
DOIs | |
State | Published - Jun 1977 |
Keywords
- Stationary point
- global minima
- optimality conditions
- point-to-set mapping