Series: Combinatorial Optimization , Vol. 12
2007, XVIII, 830 p., Softcover
ISBN: 978-0-387-44459-8
Due: January 2007
About this book
This volume, which contains chapters written by reputable
researchers, provides the state of the art in theory and
algorithms for the traveling salesman problem (TSP). The book
covers all important areas of study on TSP, including polyhedral
theory for symmetric and asymmetric TSP, branch and bound, and
branch and cut algorithms, probabilistic aspects of TSP, thorough
computational analysis of heuristic and metaheuristic algorithms,
theoretical analysis of approximation algorithms, including the
emerging area of domination analysis of algorithms, discussion of
TSP software and variations of TSP such as bottleneck TSP,
generalized TSP, prize collecting TSP, maximizing TSP,
orienteering problem, etc. The book is appropriate as a reference
work or as a main or supplemental textbook in graduate and senior
undergraduate courses and projects.
Table of contents
Preface. Contributing Authors. 1. The Traveling Salesman Problem:
Applications, Formulations and Variations; A.P. Punnen. 2.
Polyhedral Theory and Branch-and-Cut Algorithms for the Symmetric
TSP; D. Naddef. 3. Polyhedral Theory for the Asymmetric Traveling
Salesman Problem; E. Balas, M. Fischetti. 4. Exact Methods for
the Asymmetric Traveling Salesman Problem M. Fischetti, et al. 5.
Approximation Algorithms for Geometric TSP; S. Arora. 6.
Exponential Neighborhoods and Domination Analysis for the TSP; G.
Gutin, et al. 7. Probabilistic Analysis of the TSP; A.M. Frieze,
J.E. Yukich. 8. Local Search and Metaheuristics; C. Rego, F.
Glover. 9. Experimental Analysis of Heuristics for the STSP; D.S.
Johnson, L.A. McGeoch. 10. Experimental Analysis of Heuristics
for the ATSP; D.S. Johnson, et al. 11. Polynomially Solvable
Cases of the TSP; S.N. Kabadi. 12. The Maximum TSP; A. Barvinok,
et al. 13. The Generalized Traveling Salesman and Orienteering
Problems; M. Fischetti, et al. 14. The Prize Collecting Traveling
Salesman Problem and Its Applications; E. Balas. 15. The
Bottleneck TSP; S.N. Kabadi, A.P. Punnen. 16. TSP Software; A.
Lodi, A.P. Punnen. Appendix A: Sets, Graphs and Permutations.
Appendix B: Computational Complexity. References. List of Figures.
List of Tables. Index.
3rd ed., 2007, X, 292 p., 31 illus., Hardcover
ISBN: 978-3-540-49378-5
About this book
This book serves as an introductory text to optimization theory
in normed spaces. Topics of this book are existence results,
various differentiability notions together with optimality
conditions, the contingent cone, a generalization of the Lagrange
multiplier rule, duality theory, extended semidefinite
optimization, and the investigation of linear quadratic and time
minimal control problems. This textbook presents fundamentals
with particular emphasis on the application to problems in the
calculus of variations, approximation and optimal control theory.
The reader is expected to have a basic knowledge of linear
functional analysis.
Table of contents
Introduction and Problem Formulation.- Existence Theorems for
Minimal Points.- Generalized Derivatives.- Tangent Cones.-
Generalized Lagrange Multiplier Rule.- Duality.- Application to
Extended Semidefinite Optimization.- Direct Treatment of Special
Optimization Problems.- Weak Convergence.- Reflexivity of Banach
Spaces.- Hahn-Banach Theorem.- Partially Ordered Linear Spaces.
2007, XX, 401 p., 16 illus., Hardcover
ISBN: 978-3-211-49904-7
About this book
Nonstandard Analysis enhances mathematical reasoning by
introducing new ways of expression and deduction. Distinguishing
between standard and nonstandard mathematical objects, its
inventor, the eminent mathematician Abraham Robinson, settled in
1961 the centuries-old problem of how to use infinitesimals
correctly in analysis. Having also worked as an engineer, he saw
not only that his method greatly simplified mathematically
proving and teaching, but also served as a powerful tool in
modelling, analyzing and solving problems in the applied
sciences, among others by effective rescaling and by
infinitesimal discretizations.
This book reflects the progress made in the forty years since the
appearance of Robinsonfs revolutionary book Nonstandard
Analysis: in the foundations of mathematics and logic, number
theory, statistics and probability, in ordinary, partial and
stochastic differential equations and in education. The
contributions are clear and essentially self-contained.
Table of contents
Series: Oberwolfach Seminars , Vol. 35
2007, Approx. 110 p., Softcover
ISBN: 978-3-7643-8309-1
Due: February 2007
About this textbook
Tropical geometry is algebraic geometry over the semifield of
tropical numbers, i.e., the real numbers and negative infinity
enhanced with the (max,+)-arithmetics. Geometrically, tropical
varieties are much simpler than their classical counterparts. Yet
they carry information about complex and real varieties.
These notes present an introduction to tropical geometry and
contain some applications of this rapidly developing and
attractive subject. It consists of three chapters which complete
each other and give a possibility for non-specialists to make the
first steps in the subject which is not yet well represented in
the literature. The intended audience is graduate, post-graduate,
and Ph.D. students as well as established researchers in
mathematics.
Table of contents
Series: Lecture Notes in Mathematics, Vol. 1896
Subseries: Ecole d'Ete Probabilit.Saint-Flour
2007, XIV, 335 p., Softcover
ISBN: 978-3-540-48497-4
Due: March 2007
About this book
Since the impressive works of Talagrand, concentration
inequalities have been recognized as fundamental tools in several
domains such as geometry of Banach spaces or random combinatorics.
They also turn to be essential tools to develop a non asymptotic
theory in statistics, exactly as the central limit theorem and
large deviations are known to play a central part in the
asymptotic theory. An overview of a non asymptotic theory for
model selection is given here and some selected applications to
variable selection, change points detection and statistical
learning are discussed. This volume reflects the content of the
course given by P. Massart in St. Flour 2003. It is mostly self-contained
and should be readable by graduate students.
Table of contents
1. Introduction.- 2. Exponential and information inequalities.- 3.
Gaussian processes.- 4. Gaussian model selection.- 5.
Concentration inequalities.- 6. Maximal inequalities.- 7. Density
estimation via model selection.- 8. Statistical learning.-
References.- Index.
Series: Lecture Notes in Mathematics , Vol. 1905
2007, Approx. 140 p., Softcover
ISBN: 978-3-540-70780-6
Due: February 25, 2007
About this book
These lectures concentrate on (nonlinear) stochastic partial
differential equations (SPDE) of evolutionary type. All kinds of
dynamics with stochastic influence in nature or man-made complex
systems can be modelled by such equations.
To keep the technicalities minimal we confine ourselves to the
case where the noise term is given by a stochastic integral w.r.t.
a cylindrical Wiener process.But all results can be easily
generalized to SPDE with more general noises such as, for
instance, stochastic integral w.r.t. a continuous local
martingale.
There are basically three approaches to analyze SPDE: the "martingale
measure approach", the "mild solution approach"
and the "variational approach". The purpose of these
notes is to give a concise and as self-contained as possible an
introduction to the "variational approach". A large
part of necessary background material, such as definitions and
results from the theory of Hilbert spaces, are included in
appendices.
Table of contents
Motivation, Aims and Examples.- Stochastic Integral in Hilbert
spaces.- Stochastic Differential Equations in Finite Dimensions.-
A Class of Stochastic Differential Equations in Banach Spaces.-
Appendices: The Bochner Integral.- Nuclear and Hilbert-Schmidt
Operators.- Pseudo Invers of Linear Operators.- Some Tools from
Real Martingale Theory.- Weak and Strong Solutions: the Yamada-Watanabe
Theorem.- Strong, Mild and Weak Solutions.
2007, Approx. 580 p., 250 illus., Hardcover
ISBN: 978-0-387-49513-2
Due: March 2007
About this textbook
This book teaches how to use Mathematica to solve a wide variety
of problems in mathematics and physics. It is based on the
lecture notes of a course taught at the University of Illinois at
Chicago to advanced undergrad and graduate students. The book is
illustrated with many detailed examples that require the student
to construct meticulous, step-by-step, easy to read Mathematica
programs. The first part, in which the reader learns how to use a
variety of Mathematica commands, contains examples, not long
explanations; the second part contains attractive applications.
The CD-ROM presents the entire text content and interactive
examples.
Table of contents
Panorama of Mathematica.- Manipulating Numbers.- Algebra.-
Analysis.- Lists.- Graphics.- Probabilty and Statistics.-
Programming.- Egyptian Fractions.- Happy Numbers.- Mersenne
Numbers.- Multibases.- Quantum Harmonic Oscillator.- Quantum
Square Potential.- Van der Pol Oscillator.- Electrostatics.-
Motion of a Charged Particle in an Electromagnetic Field.-
Duffing Oscillator.- Negative and Complex Bases.- Tautochrone
Curves.- Keplerfs Laws.- Foucaultfs Pendulum.- Iterated
Function Systems.- Public-Key Encryption.- Julia and Mandelbrot
Sets.
Series: Birkhauser Advanced Texts / Basler Lehrbucher
2007, Approx. 600 p., Hardcover
ISBN: 978-3-7643-8146-2
Due: March 2007
About this textbook
In this book, the basic methods of nonlinear analysis are
emphasized and illustrated in simple examples. Every considered
method is motivated, explained in a general form but in the
simplest possible abstract framework. Its applications are shown,
particularly to boundary value problems for elementary ordinary
or partial differential equations. The text is organized in two
levels: a self-contained basic and, organized in appendices, an
advanced level for the more experienced reader. Exercises are an
organic part of the exposition and accompany the reader
throughout the book.
Table of contents
Preface.- 1. Preliminaries.- 2. Linear and Nonlinear Operators.-
3. Abstract Integral and Differential Calculus.- 4.- Local
Properties of Differentiable Mappings.- 5. Topological and
Monotonicity Methods.- 6. Variational Methods.- 7. Boundary Value
Problems for PDE.- Summary of Methods.- Typical Applications.-
Comparison of Bifurcation Results.- Bibliography.- Index.