Abstract
In this paper, necessary and sufficient conditions for a local minimum to be global are derived. The main result is that a real function, defined on a subset ofR n, has the property that every local minimum is global if, and only if, its level sets are lower-semicontinuous point-to-set mappings.
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Zang, I., Avriel, M. On functions whose local minima are global. J Optim Theory Appl 16, 183–190 (1975). https://doi.org/10.1007/BF01262931
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DOI: https://doi.org/10.1007/BF01262931