Nonlinear Analysis and Optimization II

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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

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