Abstract
In this chapter we first generalize convex sets by introducing the concept of starshaped sets, which is “one-step” more general than the concept of convex sets. Then we make further steps generalizing the starshaped sets to obtain path-connected sets, Φ-convex sets and some other types of generalized convex sets. The generalized convex sets will serve as a basis for defining generalized concave and convex functions, which will be introduced in the third chapter. We also pay attention to the separability of starshaped sets.KeywordsConvex ConeNonempty SubsetLinear FunctionalGeneralize ConvexFinite FamilyThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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