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| Volume 8, Number 3, December 2007, pp. 337-355 | |||||||||
| Huynh Van Ngai and Jean-Paul Penot | |||||||||
| Key words: | |||||||||
| Approximately convex function, approximately convex set, monotonicity, nonsmooth analysis, normal, projection, subdifferential | |||||||||
| Mathematices Subject Classification: Primary 49J52, 46N10, 46T20 | |||||||||
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| Abstract: | |||
| We study two classes of sets whose associated distance functions satisfy properties akin to approximate convexity. Since the class of approximately convex functions is known to enjoy nice properties, one may expect analogous properties for this class of sets. We present characterizations and delineate links with the concept of approximately convex functions through epigraphs and sublevel sets. | |||
| Approximately convex sets | ||