## Optimality Conditions: Abnormal and Degenerate ProblemsThis book is devoted to one of the main questions of the theory of extremal prob lems, namely, to necessary and sufficient extremality conditions. It is intended mostly for mathematicians and also for all those who are interested in optimiza tion problems. The book may be useful for advanced students, post-graduated students, and researchers. The book consists of four chapters. In Chap. 1 we study the abstract minimization problem with constraints, which is often called the mathemati cal programming problem. Chapter 2 is devoted to one of the most important classes of extremal problems, the optimal control problem. In the third chapter we study one of the main objects of the calculus of variations, the integral quadratic form. In the concluding, fourth, chapter we study local properties of smooth nonlinear mappings in a neighborhood of an abnormal point. The problems which are studied in this book (of course, in addition to their extremal nature) are united by our main interest being in the study of the so called abnormal or degenerate problems. This is the main distinction of the present book from a large number of books devoted to theory of extremal problems, among which there are many excellent textbooks, and books such as, e.g., [13, 38, 59, 78, 82, 86, 101, 112, 119], to mention a few. |

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### Índice

II | 1 |

III | 8 |

IV | 11 |

V | 15 |

VI | 22 |

VII | 23 |

VIII | 31 |

IX | 36 |

XXVI | 147 |

XXVII | 155 |

XXVIII | 164 |

XXIX | 167 |

XXX | 174 |

XXXI | 181 |

XXXII | 183 |

XXXIII | 188 |

X | 41 |

XI | 44 |

XII | 53 |

XIII | 60 |

XIV | 69 |

XV | 71 |

XVI | 74 |

XVII | 78 |

XVIII | 89 |

XIX | 92 |

XX | 98 |

XXI | 107 |

XXII | 115 |

XXIII | 123 |

XXIV | 133 |

XXV | 141 |

XXXIV | 196 |

XXXV | 198 |

XXXVI | 208 |

XXXVII | 221 |

XXXVIII | 242 |

XXXIX | 245 |

XL | 249 |

XLI | 258 |

XLII | 265 |

XLIII | 268 |

XLIV | 279 |

287 | |

293 | |

XLVII | 297 |

### Outras edições - Ver tudo

Optimality Conditions: Abnormal and Degenerate Problems Aram Arutyunov Pré-visualização limitada - 2013 |

Optimality Conditions: Abnormal and Degenerate Problems Aram Arutyunov Pré-visualização indisponível - 2010 |

Optimality Conditions: Abnormal and Degenerate Problems Aram Arutyunov Pré-visualização indisponível - 2012 |

### Palavras e frases frequentes

2-normal abnormal point absolutely continuous assertion assume assumption Banach space bilinear class of relaxed closed interval codim conditions with respect cone consider const construction converging to zero convex corresponding defined definition denote endpoint constraints equation example finite topology finite-dimensional subspace fixed form q form Uw formula Hilbert space implicit function theorem implies introduce into consideration Lagrange multiplier rule Lebesgue integrable Legendre condition lemma is proved linear operator mapping F mapping Q matrix maximum principle minimum point mixed constraints Moreover multi-valued mapping neighborhood nonnegative nontriviality condition normal Obviously optimal control optimal control problem optimal process point XQ positive integer positive semi-definite proof of Theorem quadratic form quadratic mapping Radon measures relations relaxed controls satisfies semicontinuous solution strong 2-regularity surjective take an arbitrary Theorem 4.1 theorem is proved transversality conditions tuple type of constraints variable weakened MP

### Referências a este livro

Variational Analysis and Generalized Differentiation I: Basic Theory Boris S. Mordukhovich Pré-visualização indisponível - 2012 |

Variational Analysis and Generalized Differentiation II: Applications Boris S. Mordukhovich Pré-visualização indisponível - 2012 |