Mordukhovich B. Variational Analysis and Generalized Diff II. Applications 2006

Textbook in PDF format

Modern variational analysis can be viewed as an outgrowth of the calculus of variations and mathematical programming, where the focus is on optimization of functions relative to various constraints and on sensitivity/stability of optimization-related problems with respect to perturbations. Classical notions of variations such as moving away from a given point or curve no longer play a critical role, while concepts of problem approximations and/or perturbations become crucial. Generalized differentiation lies at the heart of variational analysis and its applications. Volume II Applications consists of four chapters mostly devoted to applications of basic principles in variational analysis and the developed generalized differential calculus to various topics in constrained optimization and equilibria, optimal control of ordinary and distributed-parameter systems, and models of welfare economics.
Applications
Constrained Optimization and Equilibria
Optimal Control of Evolution Systems in Banach Spaces
Optimal Control of Distributed Systems
Applications to Economics
List of Statements
Glossary of Notation
Subject Index