The Cutting Planes method for abstract convexity

The cutting plane method, which only uses the global definition of the subdifferential, i.e., its support properties and it can be easily generalized for the abstract convex setting. In this paper, we first examine properties of topical (increasing and plus-homogeneous) functions defined on a normed linear space X. We also study many results of abstract convexity such as support set, polarity and subdifferential set of these functions. Finally, we consider the corresponding method as the generalized cutting plane method.

کلیدواژه ها:

Topical function ، Subdifferential ، abstract convexity ، cutting plane