# Nonlinear Analysis and Optimization II

American Mathematical Soc., 2010 - Mathematics - 290 pages
This 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 Error Bounds Calmness and their Applications in Nonsmooth Analysis 225 Commutativity of Control Vector Fields and InfCommutativity 249 Stability of Exact Penalty for Classes of Constrained Minimization Problems in FiniteDimensional Spaces 277 Copyright

 Metric Regular Maps and Regularity for Constrained Extremum Problems 143