Second-Order Generalized Differentiation Of Piecewise Linear-Quadratic Functions And Its Applications

The area of second-order variational analysis has been rapidly developing during the recent years with many important applications in optimization. This dissertation is devoted to the study and applications of the second-order generalized differentiation of a remarkable class of convex extended-real-valued functions that is highly important in many aspects of nonlinear and variational analysis, specifically those related to optimization and stability. The first goal of this dissertation is to compute the second-order subdifferential of the functions described above, which will be applied in the study of the stability of composite optimization problems associated with piecewise linear-quadratic functions, known as extended nonlinear programming (ENLPs). In the second part of the dissertation, the multiplier criticality is studied systematically for variational systems of composite optimization problems with applications to KKT systems in ENLPs