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.
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The Conjugate of Convex Functionals 27
Optimality Conditions for Convex Problems
Duality of Convex Problems
Derivatives and Subdifferentials of Lipschitz Functionals
Subdifferentials of Lower Semicontinuous Functionals
Further Topics 347