This book treats various concepts of generalized derivatives and subdifferentials in normed spaces, their geometric counterparts and their application to optimization problems. It starts with the subdifferential of convex analysis, passes to corresponding concepts for locally Lipschitz continuous functions and then presents subdifferentials for general lower semicontinuous functions. All basic tools are presented where they are needed: this concerns separation theorems, variational and extremal principles as well as relevant parts of multifunction theory. Each chapter ends with bibliographic notes and exercises.
The reader is required to have a basic knowledge of functional analysis only. All further prerequisites are presented in the book
The presentation strictly proceeds from simple to more difficult
The presentation is rigorous, with detailed proofs. Each chapter ends with suggestions for further study and with exercises