Mordukhovich B. Variational Analysis and Generalized Diff I. Basic Theory 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 I Basic Theory consists of four chapters mostly devoted to basic constructions of generalized differentiation, fundamental extremal and variational principles, comprehensive generalized differential calculus, and complete dual characterizations of fundamental properties in nonlinear study related to Lipschitzian stability and metric regularity with their applications to sensitivity analysis of constraint and variational systems.
Basic Theory
Generalized Differentiation in Banach Spaces
Extremal Principle in Variational Analysis
Full Calculus in Asplund Spaces
Characterizations of Well-Posedness and Sensitivity Analysis