Second-Order Variational Analysis in Optimization, Variational Stability, and Control: Theory, Algorithms, Applications

The book provides a detailed study of second-order subdifferentials, their calculus and efficient evaluations/ calculations for major classes of functions encountered in problems of variational analysis, optimization, etc. in finite-dimensional and infinite-dimensional spaces. These results and advanced variational techniques turn out to be instrumental in characterizing fundamental notions of variational stability of solutions for diverse classes of problems in optimization and optimal control, the study of variational convexity of extended-real-valued functions and their specifications, and variational sufficiency in optimization among other topics considered in the book. We also include in the book quite recent applications of the second-order subdifferentials, married to the achieved characterizations of variational stability and related concepts, to the design and justification of second-order numerical algorithms for solving various classes of optimization problems, nonsmooth equations, and subgradient inclusions. The developed algorithms are numerically implemented to solve some practical models taken from machine learning, statistics, imaging processes, and other applied areas.