Variational aspects of generalized convex functions
نویسندگان
چکیده
منابع مشابه
Generalized convex functions and generalized di¤erentials
We study some classes of generalized convex functions, using a generalized di¤erential approach. By this we mean a set-valued mapping which stands either for a derivative, a subdi¤erential or a pseudodi¤erential in the sense of Jeyakumar and Luc. We establish some links between the corresponding classes of pseudoconvex, quasiconvex and another class of generalized convex functions we introduced...
متن کاملGeneralized convex functions and generalized differentials
We study some classes of generalized convex functions, using a generalized di¤erential approach. By this we mean a set-valued mapping which stands either for a derivative, a subdi¤erential or a pseudodi¤erential in the sense of Jeyakumar and Luc. We establish some links between the corresponding classes of pseudoconvex, quasiconvex and another class of generalized convex functions we introduced...
متن کاملA Variational Method for Hyperbolically Convex Functions
In this paper we recall our variational method, based on Julia’s formula for the Hadamard variation, for hyperbolically convex polygons. We use this variational method to prove a general theorem for solving extremal problems for hyperbolically convex functions. Special cases of this theorem provide independent proofs for controlling growth and distortion for hyperbolically convex functions.
متن کاملVariational Gram Functions: Convex Analysis and Optimization
We propose a new class of convex penalty functions, called variational Gram functions (VGFs), that can promote pairwise relations, such as orthogonality, among a set of vectors in a vector space. These functions can serve as regularizers in convex optimization problems arising from hierarchical classification, multitask learning, and estimating vectors with disjoint supports, among other applic...
متن کاملSmoothness Properties of Generalized Convex Functions
We present a concise and elementary proof of a theorem of Karlin and Studden concerning the smoothness properties of functions belonging to a generalized convexity cone. In [1, Chapter XI], Karlin and Studden showed that a function which is convex with respect to an extended complete Tchebycheff system has a continuous derivative of order n — 1, a fact which is of considerable importance in the...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1959
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1959.9.571