## Nonsmooth AnalysisThis 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. |

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

1 | |

The Conjugate of Convex Functionals 27 | 26 |

Classical Derivatives | 39 |

Optimality Conditions for Convex Problems | 91 |

Duality of Convex Problems | 111 |

Derivatives and Subdifferentials of Lipschitz Functionals | 131 |

Variational Principles | 155 |

Subdifferentials of Lower Semicontinuous Functionals | 167 |

Further Topics 347 | 346 |

Notation | 363 |

### Other editions - View all

### Common terms and phrases

analogous Asplund space assertion Assume assumptions Borwein bounded chain rule closed subset continuously differentiable convergent convex cone convex functional convex set convex subset Corollary defined definition denotes directional derivative dual pair E X F epif equation equivalent Exercise extremal principle f is continuous f is G-differentiable f is locally finite-dimensional Fréchet smooth Banach functional f Further let G-derivative graph Hilbert space implies inequality int dom f Lemma Let f locally convex locally convex spaces locally L-continuous lower semicontinuous mapping mean value theorem minimizer of f monotone Mordukhovich multifunction NF(A nonempty subset normal cone normed vector space numbers obtain optimality conditions problem Proof Proposition Recall Remark satisfying smooth Banach space solution strong minimizer subdifferential mapping sufficiently small sum rule Tc(A topological vector space topology variational principle verify zero