On functions whose stationary points are global minima |
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| Authors: | I Zang E U Choo M Avriel |
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| Institution: | (1) Faculty of Management, Tel Aviv University, Tel Aviv, Israel;(2) Faculty of Commerce, The University of British Columbia, Vancouver, BC, Canada;(3) Department of Industrial and Management Engineering, Technion, Israel Institute of Technology, Haifa, Israel |
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| 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 ofR
n 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.The authors are thankful to an anonymous referee of an earlier version of this paper for his valuable comments. This research was partially supported by the Office of Naval Research, Contract No. N-00014-75-C-0267, by the National Science Foundation, Grant No. MPS-71-03341-A03, and by the US Energy Research and Development Administration, Contract No. E(04-3)-326 PA-18. An earlier version of this paper appeared as CORE Discussion Paper No. 7502. Part of this research was carried out while the first author was at CORE, Louvain, Belgium. |
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| Keywords: | Stationary point global minima point-to-set mapping optimality conditions |
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