Optimal Urban Networks via Mass Transportation

Optimal Urban Networks via Mass Transportation

The present monograph treats one particular class of mathematical models arising in urban planning, namely, the models of optimization of transportation networks such as urban traffic networks, networks of tram or metro lines, ...

Author: Giuseppe Buttazzo

Publisher: Springer

ISBN: 9783540857990

Category: Mathematics

Page: 150

View: 605

Recently much attention has been devoted to the optimization of transportation networks in a given geographic area. One assumes the distributions of population and of services/workplaces (i.e. the network's sources and sinks) are known, as well as the costs of movement with/without the network, and the cost of constructing/maintaining it. Both the long-term optimization and the short-term, "who goes where," optimization are considered. These models can also be adapted for the optimization of other types of networks, such as telecommunications, pipeline or drainage networks. In the monograph we study the most general problem settings, namely, when neither the shape nor even the topology of the network to be constructed is known a priori.
Categories: Mathematics

Optimal Urban Networks via Mass Transportation

Optimal Urban Networks via Mass Transportation

Recently much attention has been devoted to the optimization of transportation networks in a given geographic area.

Author: Giuseppe Buttazzo

Publisher: Springer Science & Business Media

ISBN: 9783540857983

Category: Mathematics

Page: 161

View: 668

Recently much attention has been devoted to the optimization of transportation networks in a given geographic area. One assumes the distributions of population and of services/workplaces (i.e. the network's sources and sinks) are known, as well as the costs of movement with/without the network, and the cost of constructing/maintaining it. Both the long-term optimization and the short-term, "who goes where," optimization are considered. These models can also be adapted for the optimization of other types of networks, such as telecommunications, pipeline or drainage networks. In the monograph we study the most general problem settings, namely, when neither the shape nor even the topology of the network to be constructed is known a priori.
Categories: Mathematics

Optimization and Control for Partial Differential Equations

Optimization and Control for Partial Differential Equations

Uncertainty quantification, open and closed-loop control, and shape optimization Roland Herzog, Matthias Heinkenschloss, Dante Kalise, Georg Stadler, ... Optimal Urban Networks via Mass Transportation, volume 1961 of Lecture Notes ...

Author: Roland Herzog

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 9783110695984

Category: Mathematics

Page: 474

View: 838

This book highlights new developments in the wide and growing field of partial differential equations (PDE)-constrained optimization. Optimization problems where the dynamics evolve according to a system of PDEs arise in science, engineering, and economic applications and they can take the form of inverse problems, optimal control problems or optimal design problems. This book covers new theoretical, computational as well as implementation aspects for PDE-constrained optimization problems under uncertainty, in shape optimization, and in feedback control, and it illustrates the new developments on representative problems from a variety of applications.
Categories: Mathematics

Variational Analysis in Sobolev and BV Spaces

Variational Analysis in Sobolev and BV Spaces

Optimal Urban Networks via Mass Transportation. Lecture Notes in Mathematics 1961, Springer-Verlag, Berlin, 2009. (Cited on p. 485) G. Buttazzo, F. Santambrogio. A model for the optimal planning of an urban area. SIAM J. Math.

Author: Hedy Attouch

Publisher: SIAM

ISBN: 9781611973471

Category: Mathematics

Page: 794

View: 890

This volume is an excellent guide for anyone interested in variational analysis, optimization, and PDEs. It offers a detailed presentation of the most important tools in variational analysis as well as applications to problems in geometry, mechanics, elasticity, and computer vision. This second edition covers several new topics: new section on capacity theory and elements of potential theory now includes the concepts of quasi-open sets and quasi-continuity; increased number of examples in the areas of linearized elasticity system, obstacles problems, convection-diffusion, and semilinear equations; new section on mass transportation problems and the Kantorovich relaxed formulation of the Monge problem; new subsection on stochastic homogenization establishes the mathematical tools coming from ergodic theory; and an entirely new and comprehensive chapter (17) devoted to gradient flows and the dynamical approach to equilibria. The book is intended for Ph.D. students, researchers, and practitioners who want to approach the field of variational analysis in a systematic way.
Categories: Mathematics

Nonlinear Optimization

Nonlinear Optimization

1950: M. Bramson, Stability of Queueing Networks, Ecole d'Eté de Probabilités de Saint-Flour XXXVI-2006 (2008) Vol. ... S.Solimini, E. Stepanov, Optimal Urban Networks via Mass Transportation (2009) Vol. 1962: R. Dalang, D. Khoshnevisan ...

Author: Immanuel M. Bomze

Publisher: Springer

ISBN: 9783642113390

Category: Mathematics

Page: 279

View: 136

This volume collects the expanded notes of four series of lectures given on the occasion of the CIME course on Nonlinear Optimization held in Cetraro, Italy, from July 1 to 7, 2007. The Nonlinear Optimization problem of main concern here is the problem n of determining a vector of decision variables x ? R that minimizes (ma- n mizes) an objective function f(·): R ? R,when x is restricted to belong n to some feasible setF? R , usually described by a set of equality and - n n m equality constraints: F = {x ? R : h(x)=0,h(·): R ? R ; g(x) ? 0, n p g(·): R ? R }; of course it is intended that at least one of the functions f,h,g is nonlinear. Although the problem canbe stated in verysimpleterms, its solution may result very di?cult due to the analytical properties of the functions involved and/or to the number n,m,p of variables and constraints. On the other hand, the problem has been recognized to be of main relevance in engineering, economics, and other applied sciences, so that a great lot of e?ort has been devoted to develop methods and algorithms able to solve the problem even in its more di?cult and large instances. The lectures have been given by eminent scholars, who contributed to a great extent to the development of Nonlinear Optimization theory, methods and algorithms. Namely, they are: – Professor Immanuel M.
Categories: Mathematics

Partial Inner Product Spaces

Partial Inner Product Spaces

1960: J. Lipman, M. Hashimoto, Foundations of Grothendieck Duality for Diagrams of Schemes (2009) Vol. 1961: G. Buttazzo, A. Pratelli, S.Solimini, E. Stepanov, Optimal Urban Networks via Mass Transportation (2009) Vol.

Author: J-P Antoine

Publisher: Springer

ISBN: 9783642051364

Category: Mathematics

Page: 358

View: 228

Partial Inner Product (PIP) Spaces are ubiquitous, e.g. Rigged Hilbert spaces, chains of Hilbert or Banach spaces (such as the Lebesgue spaces Lp over the real line), etc. In fact, most functional spaces used in (quantum) physics and in signal processing are of this type. The book contains a systematic analysis of PIP spaces and operators defined on them. Numerous examples are described in detail and a large bibliography is provided. Finally, the last chapters cover the many applications of PIP spaces in physics and in signal/image processing, respectively. As such, the book will be useful both for researchers in mathematics and practitioners of these disciplines.
Categories: Mathematics

Vector Fields on Singular Varieties

Vector Fields on Singular Varieties

1960: J. Lipman, M. Hashimoto, Foundations of Grothendieck Duality for Diagrams of Schemes (2009) Vol. 1961: G. Buttazzo, A. Pratelli, S. Solimini, E. Stepanov, Optimal Urban Networks via Mass Transportation (2009) Vol.

Author: Jean-Paul Brasselet

Publisher: Springer Science & Business Media

ISBN: 9783642052040

Category: Mathematics

Page: 242

View: 218

Vector fields on manifolds play a major role in mathematics and other sciences. In particular, the Poincaré-Hopf index theorem gives rise to the theory of Chern classes, key manifold-invariants in geometry and topology. It is natural to ask what is the ‘good’ notion of the index of a vector field, and of Chern classes, if the underlying space becomes singular. The question has been explored by several authors resulting in various answers, starting with the pioneering work of M.-H. Schwartz and R. MacPherson. We present these notions in the framework of the obstruction theory and the Chern-Weil theory. The interplay between these two methods is one of the main features of the monograph.
Categories: Mathematics

Introduction to Complex Reflection Groups and Their Braid Groups

Introduction to Complex Reflection Groups and Their Braid Groups

1960: J. Lipman, M. Hashimoto, Foundations of Grothendieck Duality for Diagrams of Schemes (2009) Vol. 1961: G. Buttazzo, A. Pratelli, S.Solimini, E. Stepanov, Optimal Urban Networks via Mass Transportation (2009) Vol.

Author: Michel Broué

Publisher: Springer

ISBN: 9783642111754

Category: Mathematics

Page: 144

View: 280

This book covers basic properties of complex reflection groups, such as characterization, Steinberg theorem, Gutkin-Opdam matrices, Solomon theorem and applications, including the basic findings of Springer theory on eigenspaces.
Categories: Mathematics

Computational Science and Its Applications ICCSA 2009

Computational Science and Its Applications      ICCSA 2009

Buttazzo, G., Pratelli, A., Solimini, S., Stepanov, E.: Optimal urban networks via mass transportation. Lecture Notes in Mathematics, vol. 1961. Springer, Berlin (2009) 12. Fekete, S.P., Mitchell, J.S.B., Beurer, K.: On the continuous ...

Author: Osvaldo Gervasi

Publisher: Springer Science & Business Media

ISBN: 9783642024542

Category: Computers

Page: 991

View: 629

The two-volume set LNCS 5592 and 5593 constitutes the refereed proceedings of the International Conference on Computational Science and Its Applications, ICCSA 2009, held in Seoul, Korea, in June/July, 2009. The two volumes contain papers presenting a wealth of original research results in the field of computational science, from foundational issues in computer science and mathematics to advanced applications in virtually all sciences making use of computational techniques. The topics of the fully refereed papers are structured according to the five major conference themes: computational methods, algorithms and scientific applications, high performance technical computing and networks, advanced and emerging applications, as well as information systems and information technologies. Moreover, submissions from more than 20 workshops and technical sessions contribute to this publication. These cover topics such as geographical analysis, urban modeling, spatial statistics, wireless and ad hoc networking, logical, scientific and computational aspects of pulse phenomena in transitions, high-performance computing and information visualization, sensor network and its applications, molecular simulations structures and processes, collective evolutionary systems, software engineering processes and applications, molecular simulations structures and processes, internet communication security, security and privacy in pervasive computing environments, and mobile communications.
Categories: Computers

Spectral Theory of Non Commutative Harmonic Oscillators An Introduction

Spectral Theory of Non Commutative Harmonic Oscillators  An Introduction

1961: G. Buttazzo, A. Pratelli, S.Solimini, E. Stepanov, Optimal Urban Networks via Mass Transportation (2009) Vol. 1962: R. Dalang, D. Khoshnevisan, C. Mueller, D. Nualart, Y. Xiao, A Minicourse on Stochastic Partial Differential ...

Author: Alberto Parmeggiani

Publisher: Springer

ISBN: 9783642119224

Category: Mathematics

Page: 260

View: 326

This book grew out of a series of lectures given at the Mathematics Department of Kyushu University in the Fall 2006, within the support of the 21st Century COE Program (2003–2007) “Development of Dynamical Mathematics with High Fu- tionality” (Program Leader: prof. Mitsuhiro Nakao). It was initially published as the Kyushu University COE Lecture Note n- ber 8 (COE Lecture Note, 8. Kyushu University, The 21st Century COE Program “DMHF”, Fukuoka, 2008. vi+234 pp.), and in the present form is an extended v- sion of it (in particular, I have added a section dedicated to the Maslov index). The book is intended as a rapid (though not so straightforward) pseudodiff- ential introduction to the spectral theory of certain systems, mainly of the form a +a where the entries of a are homogeneous polynomials of degree 2 in the 2 0 2 n n (x,?)-variables, (x,?)? R×R,and a is a constant matrix, the so-called non- 0 commutative harmonic oscillators, with particular emphasis on a class of systems introduced by M. Wakayama and myself about ten years ago. The class of n- commutative harmonic oscillators is very rich, and many problems are still open, and worth of being pursued.
Categories: Mathematics