Radiant Separation Theorems and Minimum-Type Subdifferentials of Calm Functions

Applying minimum-type functions and plus-cogauges, we construct a closed, convex cone in order to separate a boundary point of a radiant set from its interior. Abstract convexity of positively homogeneous functions is studied as well. Since a locally Lipschitz function is degree-one calm, the class of degree-one calm functions is large. We study degree-one calm functions and investigate how these functions can be generated by a class of min-type functions. Then, we derive a method to find an element of the subdifferential of a non-negative, lower semicontinuous and degree-one calm function with respect to the class of min-type functions.