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Second-order characterization of convex functions and its applications

Nadi Mohammad Taghi, Yao Jen Chih, Zafarani Jafar

Journal of Applied Analysis

2019

Vol. 25, nr 1

49--58

Some developments of the second-order characterizations of convex functions are investigated by using the coderivative of the subdifferential mapping. Furthermore, some applications of the second-order subdifferentials in optimization problems are studied.

Calculus of second-order subdifferentials in infinite dimensions

Morduhovic B.

Control and Cybernetics

2002

Vol. 31, no 3

557-573

We study two types of second-order subdifferentials of extended-real-valued functions on Banach spaces that are important for applications in variational analysis, especially to sensitivity issues and second-order optimality conditions. The main concern of the paper is to derive extended sum and chain rules for these subdifferentials in the case of Asplund and general Banach spaces, which provide the basis for further theory and applications.