Abstract
In this note, we introduce a new class of generalized convex functions and show that a real functionf which is continuous on a compact convex subsetM of ℝn and whose set of global minimizers onM is arcwise-connected has the property that every local minimum is global if, and only if,f belongs to that class of functions.
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Communicated by M. Avriel
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Horst, R. A note on functions whose local minima are global. J Optim Theory Appl 36, 457–463 (1982). https://doi.org/10.1007/BF00934358
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DOI: https://doi.org/10.1007/BF00934358