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Książka Second-Order Variational Analysis in Optimization, Variational Stability, and Control Boris S. Mordukhovich

Second-Order Variational Analysis in Optimization, Variational Stability, and Control

Autor: Boris S. Mordukhovich
Język: Angielski
Oprawa: Miękka
Wydawca: Springer International Publishing
Dostępność: Na zamówienie
Wysyłamy za 17-27 dni
754.07 zł
This fundamental work is a sequel to monographs by the same author: Variational Analysis and Applica...

Informacje o książce

Autor
Boris S. Mordukhovich
Język
Angielski
Oprawa
Książka - Miękka
Data wydania
2025
strony
808
EAN
9783031534782
ISBN
3031534786
Enbook ID
49083156
Wydawca
Springer International Publishing
Waga
1200
Wymiary
155 x 235 x 44

Pełny opis

This fundamental work is a sequel to monographs by the same author: Variational Analysis and Applications (2018) and the two Grundlehren volumes Variational Analysis and Generalized Differentiation: I Basic Theory, II Applications (2006). This present book is the first entirely devoted to second-order variational analysis with numerical algorithms and applications to practical models. It covers a wide range of topics including theoretical, numerical, and implementations that will interest researchers in analysis, applied mathematics, mathematical economics, engineering, and optimization. Inclusion of a variety of exercises and commentaries in each chapter allows the book to be used effectively in a course on this subject. This area has been well recognized as an important and rapidly developing area of nonlinear analysis and optimization with numerous applications. Consisting of 9 interrelated chapters, the book is self-contained with the inclusion of some preliminaries in Chapter 1.
Results presented are useful tools for characterizations of 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.  Explicit calculations and important applications of second-order subdifferentials associated with 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 systems, are included. Generalized Newtonian algorithms are presented that show local and global convergence with linear, superlinear, and quadratic convergence rates. Algorithms are implemented to address interesting practical problems from the fields of machine learning, statistics, imaging, and other areas.

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