In this paper, new classes of generalized convex functions are introduced, extending the concepts of quasi-convexity, pseudoconvexity, and their associate subclasses. Functions belonging to these classes satisfy certain local-global minimum properties. Conversely, it is shown that, under some mild regularity conditions, functions for which the local-global minimum properties hold must belong to one of the classes of functions introduced.
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Dedicated to R. Bellman
The authors are indebted to I. Kozma, N. Megiddo, and A. Tamir for valuable discussions and to S. Schaible for valuable remarks. This research was partially supported by the Fund for the Encouragement of Research at the Technion.
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Avriel, M., Zang, I. Generalized arcwise-connected functions and characterizations of local-global minimum properties. J Optim Theory Appl 32, 407–425 (1980). https://doi.org/10.1007/BF00934030
- Generalized convexity
- global minimality
- nonlinear programming
- nonconvex programming
- optimization theorems