## Nonlinear Analysis and Optimization IIThis volume is the second of two volumes representing leading themes of current research in nonlinear analysis and optimization. The articles are written by prominent researchers in these two areas and bring the readers, advanced graduate students and researchers alike, to the frontline of the vigorous research in important fields of mathematics. This volume contains articles on optimization. Topics covered include the calculus of variations, constrained optimization problems, mathematical economics, metric regularity, nonsmooth analysis, optimal control, subdifferential calculus, time scales and transportation traffic. The companion volume (Contemporary Mathematics, Volume 513) is devoted to nonlinear analysis. This book is co-published with Bar-Ilan University (Ramat-Gan, Israel). Table of Contents: J.-P. Aubin and S. Martin -- Travel time tubes regulating transportation traffic; R. Baier and E. Farkhi -- The directed subdifferential of DC functions; Z. Balanov, W. Krawcewicz, and H. Ruan -- Periodic solutions to $O(2)$-symmetric variational problems: $O(2) \times S^1$- equivariant gradient degree approach; J. F. Bonnans and N. P. Osmolovskii -- Quadratic growth conditions in optimal control problems; J. M. Borwein and S. Sciffer -- An explicit non-expansive function whose subdifferential is the entire dual ball; G. Buttazzo and G. Carlier -- Optimal spatial pricing strategies with transportation costs; R. A. C. Ferreira and D. F. M. Torres -- Isoperimetric problems of the calculus of variations on time scales; M. Foss and N. Randriampiry -- Some two-dimensional $\mathcal A$-quasiaffine functions; F. Giannessi, A. Moldovan, and L. Pellegrini -- Metric regular maps and regularity for constrained extremum problems; V. Y. Glizer -- Linear-quadratic optimal control problem for singularly perturbed systems with small delays; T. Maruyama -- Existence of periodic solutions for Kaldorian business fluctuations; D. Mozyrska and E. Paw'uszewicz -- Delta and nabla monomials and generalized polynomial series on time scales; D. Pallaschke and R. Urba'ski -- Morse indexes for piecewise linear functions; J.-P. Penot -- Error bounds, calmness and their applications in nonsmooth analysis; F. Rampazzo -- Commutativity of control vector fields and ""inf-commutativity""; A. J. Zaslavski -- Stability of exact penalty for classes of constrained minimization problems in finite-dimensional spaces. (CONM/514) |

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### Contents

Travel Time Tubes Regulating Transportation Traffic | 1 |

The Directed Subdifferential of DC Functions | 27 |

O2 S1Equivariant Gradient Degree Approach | 45 |

Quadratic Growth Conditions in Optimal Control Problems | 85 |

An Explicit Nonexpansive Function whose Subdifferential is the Entire Dual Ball | 99 |

Optimal Spatial Pricing Strategies with Transportation Costs | 105 |

Isoperimetric Problems of the Calculus of Variations on Time Scales | 123 |

Some TwoDimensional AQuasiaffine Functions | 133 |

LinearQuadratic Optimal Control Problem for Singularly Perturbed Systems with Small Delays | 155 |

Existence of Periodic Solutions for Kaldorian Business Fluctuations | 189 |

Delta and Nabla Monomials and Generalized Polynomial Series on Time Scales | 199 |

Morse Indexes for Piecewise Linear Functions | 213 |

225 | |

Commutativity of Control Vector Fields and InfCommutativity | 249 |

Stability of Exact Penalty for Classes of Constrained Minimization Problems in FiniteDimensional Spaces | 277 |

Metric Regular Maps and Regularity for Constrained Extremum Problems | 143 |

### Other editions - View all

Nonlinear analysis and optimization : a Conference in Celebration ..., Volume 2 Arie Leizarowitz No preview available - 2010 |

### Common terms and phrases

analysis applications associated assume assumptions Banach space bounded calculus called characterization closed compact computations condition cone connected consider constant constraints continuous convex corresponding cost critical defined DEFINITION denote derivative difference directed equation equivalent evolution example exists fact finite fixed formula function function f given gradient Hence holds implies inequality interval introduce Lemma linear Lipschitz lower Math Mathematics matrix maximal means metrically regular multi-time Nonlinear Note Observe obtain operator optimal optimal control partial particular perturbed positive problem PROOF Proposition prove REMARK resp respect ring satisfies scales sequence solution space strong subdifferential subset sufficient Suppose Theorem theory tion tube unique University variational vector fields weak