This book provides a self-contained, comprehensive and up-to-date presentation of uncertainty theory. The purpose is to equip the readers with an axiomatic approach to deal with uncertainty. For this new edition the entire text has been totally rewritten. The chapters on chance theory and uncertainty theory are completely new. Mathematicians, researchers, engineers, designers, and students will find this work a stimulating and useful reference.

This book examines the main methodological and theoretical developments in stochastic global optimization. It is designed to inspire readers to explore various stochastic methods of global optimization by clearly explaining the main methodological principles and features of the methods. Among the book 's features is a comprehensive study of probabilistic and statistical models underlying the stochastic optimization algorithms.

This book is a tutorial survey of the methodologies that are at the confluence of several fields: Computer Science, Mathematics and Operations Research. It provides a carefully structured and integrated treatment of the major technologies in optimization and search methodology. The chapter authors are drawn from across Computer Science and Operations Research and include some of the world 's leading authorities in their field. It can be used as a textbook or a reference book to learn and apply these methodologies to a wide range of today 's problems.

This text develops the mathematical implications of barriers to the geometrical and analytical characteristics of continuous location problems. The book will appeal to those working in operations research and management science, and mathematicians interested in optimization theory and its applications.

A collection of 28 refereed papers grouped according to four broad topics: duality and optimality conditions, optimization algorithms, optimal control, and variational inequality and equilibrium problems. Suitable for researchers, practitioners and postgrads.

Switched linear systems have enjoyed a particular growth in interest since the 1990s. The large amount of data and ideas thus generated have, until now, lacked a co-ordinating framework to focus them effectively on some of the fundamental issues such as the problems of robust stabilizing switching design, feedback stabilization and optimal switching.

This deficiency is resolved by this book which features: nucleus of constructive design approaches based on canonical decomposition and forming a sound basis for the systematic treatment of secondary results; theoretical exploration and logical association of several independent but pivotal concerns in control design as they pertain to switched linear systems: controllability and observability, feedback stabilization, optimization and periodic switching; a reliable foundation for further theoretical research as well as design guidance for real life engineering applications through the integration of novel ideas, fresh insights and rigorous results.

The editors and authors dedicate this book to Bernhard Korte on the occasion of his seventieth birthday. We, the editors, are happy about the overwhelming feedback to our initiative to honor him with this book and with a workshop in Bonn on November 3-7,2008.Althoughthiswouldbeareasontolookback, wewouldratherliketolook forward and see what are the interesting research directions today. This book is written by leading experts in combinatorial optimization. All - pers were carefully reviewed, and eventually twenty-three of the invited papers were accepted for this book. The breadth of topics is typical for the eld: combinatorial optimization builds bridges between areas like combinatorics and graph theory, submodular functions and matroids, network ows and connectivity, approximation algorithms and mat- matical programming, computational geometry and polyhedral combinatorics. All these topics are related, and they are all addressed in this book. Combi- torial optimization is also known for its numerous applications. To limit the scope, however, this book is not primarily about applications, although some are mentioned at various places. Most papers in this volume are surveys that provide an excellent overview of an activeresearcharea, butthisbookalsocontainsmanynewresults.Highlightingmany of the currently most interesting research directions in combinatorial optimization, we hope that this book constitutes a good basis for future research in these area

The international conference \Operations Research 2008," the annual meeting of the German Operations Research Society (GOR), was held at the University of Augsburg on September 3-5, 2008. About 580 p- ticipants from more than 30 countries presented and listened to nearly 400 talks on a broad range of Operations Research. The general subject \Operations Research and Global Business" str- ses the important role of Operations Research in improving decisions in the increasingly complex business processes in a global environment. The plenary speakers Morris A. Cohen (Wharton School) and Bernd Liepert (Executive Board of KUKA Robotics) addressed this subject. Moreover, one of the founders of Operations Research, Saul Gass (U- versity of Maryland), gave the opening speech on the early history of Operations Research. This volume contains 93 papers presented at the conference, selected by the program committee and the section chairs, forming a representative sample of the various subjects dealt with at Operations Research 2008. The volume follows the structure of the conference, with 12 sections, grouped into six \Fields of Applications" and six \Fields of Methods and Theory." This structure in no way means a separation of theory and application, which would be detrimental in Operations Research, but displays the large spectrum of aspects in the focus of the papers. Of course, most papers present theory, methods and applications together.

The results presented in this book originate from the last decade research work of the author in the ?eld of duality theory in convex optimization. The reputation of duality in the optimization theory comes mainly from the major role that it plays in formulating necessary and suf?cient optimality conditions and, consequently, in generatingdifferent algorithmic approachesfor solving mathematical programming problems. The investigations made in this work prove the importance of the duality theory beyond these aspects and emphasize its strong connections with different topics in convex analysis, nonlinear analysis, functional analysis and in the theory of monotone operators. The ?rst part of the book brings to the attention of the reader the perturbation approach as a fundamental tool for developing the so-called conjugate duality t- ory. The classical Lagrange and Fenchel duality approaches are particular instances of this general concept. More than that, the generalized interior point regularity conditions stated in the past for the two mentioned situations turn out to be p- ticularizations of the ones given in this general setting. In our investigations, the perturbationapproachrepresentsthestartingpointforderivingnewdualityconcepts for several classes of convex optimization problems. Moreover, via this approach, generalized Moreau-Rockafellar formulae are provided and, in connection with them, a new class of regularity conditions, called closedness-type conditions, for both stable strong duality and strong duality is introduced. By stable strong duality we understand the situation in which strong duality still holds whenever perturbing the objective function of the primal problem with a linear continuous functional.

physics

George Dantzig is widely regarded as the founder of this subject with his invention of the simplex algorithm in the 1940's. In this second volume, the theory of the items discussed in the first volume is expanded to include such additional advanced topics as variants of the simplex method; interior point methods, GUB, decomposition, integer programming, and game theory. Graduate students in the fields of operations research, industrial engineering and applied mathematics will thus find this volume of particular interest.

In the twenty-first century the sustainability of energy and transportation systems is on the top of the political agenda in many countries around the world.

Environmental impacts of human economic activity necessitate the consideration of conflicting goals in decision making processes to develop sustainable systems. Any sustainable development has to reconcile conflicting economic and environmental objectives and criteria. The science of multiple criteria decision making has a lot to offer in addressing this need. Decision making with multiple (conflicting) criteria is the topic of research that is at the heart of the International Society of Multiple Criteria Decision Making. This book is based on selected papers presented at the societies 19th International Conference, held at The University of Auckland, New Zealand, from 7th to 12th January 2008 under the theme "MCDM for Sustainable Energy and Transportation Systems''.

Support for addressing the on-going global changes needs solutions for new scientific problems which in turn require new concepts and tools. A key issue concerns a vast variety of irreducible uncertainties, including extreme events of high multidimensional consequences, e.g., the climate change. The dilemma is concerned with enormous costs versus massive uncertainties of extreme impacts. Traditional scientific approaches rely on real observations and experiments. Yet no sufficient observations exist for new problems, and "pure" experiments, and learning by doing may be expensive, dangerous, or impossible. In addition, the available historical observations are often contaminated by past actions, and policies. Thus, tools are presented for the explicit treatment of uncertainties using "synthetic" information composed of available "hard" data from historical observations, the results of possible experiments, and scientific facts, as well as "soft" data from experts' opinions, and scenarios.

The problem of stochastic control of partially observable systems plays an important role in many applications. All real problems are in fact of this type, and deterministic control as well as stochastic control with full observation can only be approximations to the real world. This justifies the importance of having a theory as complete as possible, which can be used for numerical implementation. This book first presents those problems under the linear theory that may be dealt with algebraically. Later chapters discuss the nonlinear filtering theory, in which the statistics are infinite dimensional and thus, approximations and perturbation methods are developed.

In the latter part of the twentieth century, the topic of generalizations of convexfunctions has attracted a sizable number of researchers,both in ma- ematics and in professional disciplines such as economics/management and engineering. In 1994 during the 15th International Symposium on Mathem- ical Programming in Ann Arbor, Michigan, I called together some colleagues to start an a?liation of researchers working in generalized convexity. The international Working Group of Generalized Convexity (WGGC) was born. Its website at www.genconv.org has been maintained by Riccardo Cambini, University of Pisa. Riccardo's father, Alberto Cambini, and Alberto's long-term colleague Laura Martein in the Faculty of Economics, University of Pisa, are the - authors of this volume. My own contact with generalized convexity in Italy datesbacktomy?rstvisittotheirdepartmentin1980,atatimewhenthe?rst international conference on generalized convexity was in preparation. Thirty years later it is now referred to as GC1, an NATO Summer School in V- couver, Canada. Currently WGGC is preparing GC9 which is to take place in Kaohsiung, Taiwan. As founding chair and also current chair of WGGC, I am delighted to see the continued interest in generalized convexity of functions, augmented by the topic of generalized monotonicity of maps. Eight international conferences have taken place in this research area, in North America (2), Europe (5) and Asia (1). We thought it was now time to return to Asia since our membership has shifted towards Asia. AsanappliedmathematicianIhavetaughtmostlyinmanagementschools.

Optimization is concerned with finding the best (optimal) solution to mathematical problems that may arise in economics, engineering, the social sciences and the mathematical sciences. As is suggested by its title, this book surveys various ways of penetrating the subject. The author begins with a selection of the type of problem to which optimization can be applied and the remainder of the book develops the theory, mainly from the viewpoint of mathematical programming. To prevent the treatment becoming too abstract, subjects which may be considered 'unpractical' are not touched upon. The author gives plausible reasons, without forsaking rigor, to show how the subject develops 'naturally'. Professor Ponstein has provided a concise account of optimization which should be readily accessible to anyone with a basic understanding of topology and functional analysis. Advanced students and professionals concerned with operations research, optimal control and mathematical programming will welcome this useful and interesting book.

Jon Lee focuses on key mathematical ideas leading to useful models and algorithms, rather than on data structures and implementation details, in this introductory graduate-level text for students of operations research, mathematics, and computer science. The viewpoint is polyhedral, and Lee also uses matroids as a unifying idea. Topics include linear and integer programming, polytopes, matroids and matroid optimization, shortest paths, and network flows. Problems and exercises are included throughout as well as references for further study.

Jon Lee focuses on key mathematical ideas leading to useful models and algorithms, rather than on data structures and implementation details, in this introductory graduate-level text for students of operations research, mathematics, and computer science. The viewpoint is polyhedral, and Lee also uses matroids as a unifying idea. Topics include linear and integer programming, polytopes, matroids and matroid optimization, shortest paths, and network flows. Problems and exercises are included throughout as well as references for further study.

What is the shortest possible route for a traveling salesman seeking to visit each city on a list exactly once and return to his city of origin? It sounds simple enough, yet the traveling salesman problem is one of the most intensely studied puzzles in applied mathematics--and it has defied solution to this day. In this book, William Cook takes readers on a mathematical excursion, picking up the salesman's trail in the 1800s when Irish mathematician W. R. Hamilton first defined the problem, and venturing to the furthest limits of today's state-of-the-art attempts to solve it. He also explores its many important applications, from genome sequencing and designing computer processors to arranging music and hunting for planets.

"In Pursuit of the Traveling Salesman" travels to the very threshold of our understanding about the nature of complexity, and challenges you yourself to discover the solution to this captivating mathematical problem.

This volume is dedicated to the centenary of the outstanding mathematician of the 20th century, Sergey Sobolev, and, in a sense, to his celebrated work On a theorem of functional analysis, published in 1938, exactly 70 years ago, was where the original Sobolev inequality was proved. This double event is a good occasion to gather experts for presenting the latest results on the study of Sobolev inequalities, which play a fundamental role in analysis, the theory of partial differential equations, mathematical physics, and differential geometry. In particular, the following topics are discussed: Sobolev-type inequalities on manifolds and metric measure spaces, traces, inequalities with weights, unfamiliar settings of Sobolev type inequalities, Sobolev mappings between manifolds and vector spaces, properties of maximal functions in Sobolev spaces, the sharpness of constants in inequalities, etc.

The volume opens with a nice survey reminiscence, "My Love Affair with the Sobolev Inequality," by David R. Adams.

Metaheuristics have been shown to be e?ective for di?cult combinatorial - timization problems appearing in various industrial, economical, and scienti?c domains. Prominent examples of metaheuristics are evolutionary algorithms, tabu search, simulated annealing, scatter search, memetic algorithms, variable neighborhood search, iterated local search, greedy randomized adaptive search procedures, ant colony optimization and estimation of distribution algorithms. Problems solved successfully include scheduling, timetabling, network design, transportation and distribution, vehicle routing, the travelling salesman pr- lem, packing and cutting, satis?ability and general mixed integer programming. EvoCOPbeganin2001andhasbeenheldannuallysincethen.Itwasthe?rst event speci?cally dedicated to the application of evolutionary computation and related methods to combinatorial optimization problems. Originally held as a workshop, EvoCOPbecameaconferencein2004.Theeventsgaveresearchersan excellent opportunity to present their latest research and to discuss current - velopments and applications. Following the general trend of hybrid metaheur- tics and diminishing boundaries between the di?erent classes of metaheuristics, EvoCOP has broadened its scope over the last years and invited submissions on any kind of metaheuristic for combinatorial optimization

This book revises the well-known capacity control problem in revenue management from the perspective of a risk-averse decision-maker. Modelling an expected utility maximizing decision maker, the problem is formulated as a risk-sensitive Markov decision process. Special emphasis is put on the existence of structured optimal policies. Numerical examples illustrate the results.

The Fifth International Conference on Automatic Differentiation held from August 11 to 15, 2008 in Bonn, Germany, is the most recent one in a series that began in Breckenridge, USA, in 1991 and continued in Santa Fe, USA, in 1996, Nice, France, in 2000 and Chicago, USA, in 2004. The 31 papers included in these proceedings re?ect the state of the art in automatic differentiation (AD) with respect to theory, applications, and tool development. Overall, 53 authors from institutions in 9 countries contributed, demonstrating the worldwide acceptance of AD technology in computational science. Recently it was shown that the problem underlying AD is indeed NP-hard, f- mally proving the inherently challenging nature of this technology. So, most likely, no deterministic "silver bullet" polynomial algorithm can be devised that delivers optimum performance for general codes. In this context, the exploitation of doma- speci?c structural information is a driving issue in advancing practical AD tool and algorithm development. This trend is prominently re?ected in many of the pub- cations in this volume, not only in a better understanding of the interplay of AD and certain mathematical paradigms, but in particular in the use of hierarchical AD approaches that judiciously employ general AD techniques in application-speci?c - gorithmic harnesses. In this context, the understanding of structures such as sparsity of derivatives, or generalizations of this concept like scarcity, plays a critical role, in particular for higher derivative computations.

Financial globalization has increased the significance of methods used in the evaluation of country risk, one of the major research topics in economics and finance. Written by experts in the fields of multicriteria methodology, credit risk assessment, operations research, and financial management, this book develops a comprehensive framework for evaluating models based on several classification techniques that emerge from different theoretical directions. This book compares different statistical and data mining techniques, noting the advantages of each method, and introduces new multicriteria methodologies that are important to country risk modeling. Key topics include: (1) A review of country risk definitions and an overview of the most recent tools in country risk management, (2) In-depth analysis of statistical, econometric and non-parametric classification techniques, (3) Several real-world applications of the methodologies described throughout the text, (4) Future research directions for country risk assessment problems. This work is a useful toolkit for economists, financial managers, bank managers, operations researchers, management scientists, and risk analysts. Moreover, the book can also be used as a supplementary text for graduate courses in finance and financial risk management.

This book constitutes the refereed proceedings of the 7th European Conference on Evolutionary Computation in Combinatorial Optimization, EvoCOP 2007, held in Valencia, Spain in April 2007. The 21 revised full papers cover evolutionary algorithms as well as various other metaheuristics, like scatter search, tabu search, memetic algorithms, variable neighborhood search, ant colony optimization, and particle swarm optimization algorithms.