Book Description

The focus of this book is on bilevel programming which combines elements of hierarchical optimization and game theory. The basic model addresses the problem where two decision-makers, each with their individual objectives, act and react in a noncooperative manner. The actions of one affect the choices and payoffs available to the other but neither player can completely dominate the other in the traditional sense. Over the last 20 years there has been a steady growth in research related to theory and solution methodologies for bilevel programming. This interest stems from the inherent complexity and consequent challenge of the underlying mathematics, as well as the applicability of the bilevel model to many real-world situations. The primary aim of this book is to provide a historical perspective on algorithmic development and to highlight those implementations that have proved to be the most efficient in their class. A corollary aim is to provide a sampling of applications in order to demonstrate the versatility of the basic model and the limitations of current technology.What is unique about this book is its comprehensive and integrated treatment of theory, algorithms and implementation issues. It is the first text that offers researchers and practitioners an elementary understanding of how to solve bilevel programs and a perspective on what success has been achieved in the field.Audience: Includes management scientists, operations researchers, industrial engineers, mathematicians and economists. ... Read more

Book Description

The aim of Cooperative Games on Combinatorial Structures is to analyze conflict situations in which two or more players can make coalitions and obtain prizes and penalties. This approach to situations of competition and cooperation was given in the seminal treatise by John von Neumann and Oskar Morgenstern, Theory of Games and Economic Behavior. Cooperative game theory has succeeded in providing many applications of game theory.In this volume, games defined on combinatorial structures will be analyzed, i.e. a set system over a set of players. In many situations the author will work in a closure space. Examples of closure operators are the spanning operator of linear algebra and all convex hull operators.Chapters 1--4 constitute a review of mathematical concepts from Cooperative Game Theory, Graph Theory, Linear and Integer Programming, Combinatorial Optimization, Discrete Convex Analysis and Computational Complexity. The table of contents is a short guide to the topics and methods covered in this book. In Chapters 11 and 12, several notebooks are presented with the system Mathematica by Wolfram in the contexts of the packages DiscreteMath (Skiena) and Cooperative (Carter). There will also be found in the book several research projects. These are intended to offer new ideas that the reader should consider with caution.This book will be of interest to graduate students with some experience in game theory or mathematical programming and professional researchers in game theory, operational research and its applications in economic theory, and the political and social sciences. In addition, it will be especially useful for professionals who are interested in models for understanding and managing conflicts: management and operational research scientists, political and military scientists, and professional negotiators. ... Read more

Book Description

This textbook is an introduction to dynamical systems and its applications to evolutionary game theory, mathematical ecology, and population genetics. This first English edition is a translation from the authors' successful German edition which has already made an enormous impact on the teaching and study of mathematical biology. The book's main theme is to discuss the solution of differential equations that arise from examples in evolutionary biology. Topics covered include the Hardy-Weinberg law, the Lotka-Volterra equations for ecological models, genetic evolution, aspects of sociobiology, and mutation and recombination. There are numerous examples and exercises throughout and the reader is led up to some of the most recent developments in the field. Thus the book will make an ideal introduction to the subject for graduate students in mathematics and biology coming to the subject for the first time. Research workers in evolutionary theory will also find much of interest here in the application of powerful mathematical techniques to the subject. ... Read more

Book Description

This is the second in a series of contributed, refereed volumes devoted to research in optimization by Australian researchers and their collaborators. These volumes are intended to have wide scope and include survey papers by established researchers providing up-to-date information on research directions.This volume includes survey and research papers on theories and methods of nonlinear programming, nonconvex and discrete optimization, stochastic linear programming, generalized convexity, complementarity and vector variational inequality problems, dynamic systems and optimal control and applications to traffic assignment models, train control, manufacturing systems and substrate diffusion of cutaneous tissue.Audience: Practitioners, postgraduate students and researchers in optimization. ... Read more

Book Description

The book deals with modern aspects of traffic theory and its applications to real world problems. In 17 articles various new developments are reported. The topics range from microscopic computer simulation of traffic flow simulations to air pollution in urban street networks. The articles, with many illustrations are aimed at interested students as well as experts in the field. The current status of the work in this research area is presented by well-known experts. ... Read more

Book Description

This volume contains refereed papers based on lectures presented at the XIV International Conference on Mathematical Programming, held at Matrahaza, Hungary. The main purpose of the conference was to review and discuss recent advances and promising research trends concerning theory, algorithms, and applications in the fields of optimization theory, and related areas such as convex analysis, complementarity systems, and variational inequalities.Audience: Researchers in operations research, economics, mathematics, physics, and engineering. ... Read more

Book Description

This comprehensive textbook on combinatorial optimization puts special emphasis on theoretical results and algorithms with provably good performance, in contrast to heuristics. It has arisen as the basis of several courses on combinatorial optimization and more special topics at graduate level. Since the complete book contains enough material for at least four semesters (4 hours a week), one usually selects material in a suitable way. The book contains complete (but concise) proofs, also for many deep results, some of which did not appear in a book before. Many very recent topics are covered as well, and many references are provided. Thus this book represents the state-of-the-art of combinatorial optimization. ... Read more

Reviews (1)

Useful yet dense!
This is the most comprehensive compilation on combinatorial optiomization I have seen so far.
Usually, Papadimitriou's book is a good place for this material - but in many cases, looking for proofs and theorems - I had to use several books:
(*) Combinatorial Optimization Algorithms and Complexity by Papadimitriou and Steiglitz.
(*) Integer and Combinatorial Optimization by Nemhauser and Wolsey
(*) Theory of linear and integer programming by Schrijver
(*) Combinatorial Optimization by Cook, Cunningham, Pulleyblank and Schrijver
(*)Combinatorial Algorithms by Kreher and Stinson

This book, on the other hand, contains so much information and so many proved theorems - it's the richest resuorce in this topic, in my humble opinion.

Using it as a graduate level textbook for an *introduction* to combinatorial optimization is kind of hard - as although it's richness, some topics are described without enough detail or examples (like the topics on network flow and bipartite graphs) - yet the authors probably assumed some previous knowledge in those topics.

I prefer using this book as a reference rather than and intoduction.

The heavy mathematical notations in this book might scare some readers, but no-fear! You quickly get used to it, and appreciate the greatness in the notations, as they make the theorems more short and to the point. On the other hand - getting back to this book for a quick review on some subject might force you to flip pages for a fwe minutes, just to remember the notation again.

The authors intended this book to be a graduaet level textbook or an up-to-date reference work for current research. I believe they accomplished both targets! ... Read more

Book Description

Games and Decision Making is the first book to cover in one volume traditional optimization and game theory, along with such key business topics as "auctions" and "bargaining." It also features important concepts that are usually covered at a much higher level of sophistication. ... Read more

Reviews (1)

Great Analysis
Very good textbook for Game Theory class at the upper college level. ... Read more

Book Description

The order and presentation of Foundations of Queueing Theory is drawn from Professor Prabhu's extensive experience as a researcher, teacher, expositor, and editor. The book deals with the foundations of queueing theory and is intended as an advanced text for courses on queueing theory, and as a professional reference to queueing research. The results of queueing theory are established within the context of the book's instructional framework. The central results of queueing theory are stated in the form of theorems for accessibility and reading ease.Current research has shown the need to pay more attention to the basic concepts and techniques of queueing theory. These include the busy period, imbedded chains, regeneration points, Wiener--Hopf technique, time-reversibility, output, vector Markov processes, remaining workload and completion times. The use of these concepts and techniques considerably simplifies the analysis of models involving last come, first served queue discipline, priorities, networks, set-up times and server vacations. It is these conceptional techniques that form the foundations of queueing theory. ... Read more

Book Description

Simple games are mathematical structures inspired by voting systems in which a single alternative, such as a bill, is pitted against the status quo. The first in-depth mathematical study of the subject as a coherent subfield of finite combinatorics--one with its own organized body of techniques and results--this book blends new theorems with some of the striking results from threshold logic, making all of it accessible to game theorists. Introductory material receives a fresh treatment, with an emphasis on Boolean subgames and the Rudin-Keisler order as unifying concepts. Advanced material focuses on the surprisingly wide variety of properties related to the weightedness of a game.

A desirability relation orders the individuals or coalitions of a game according to their influence in the corresponding voting system. As Taylor and Zwicker show, acyclicity of such a relation approximates weightedness--the more sensitive the relation, the closer the approximation. A trade is an exchange of players among coalitions, and robustness under such trades is equivalent to weightedness of the game. Robustness under trades that fit some restrictive exchange pattern typically characterizes a wider class of simple games--for example, games for which some particular desirability order is acyclic. Finally, one can often describe these wider classes of simple games by weakening the total additivity of a weighting to obtain what is called a pseudoweighting. In providing such uniform explanations for many of the structural properties of simple games, this book showcases numerous new techniques and results. ... Read more

Reviews (1)

Good mathematics
A very well written book. The mathematical level is hard, but always such, that with a good graduate background, one can follow the proofs.
The subject matter of course is very special, a lot more special, than the editorial introduction seems to suggest.

If one either enjoys mathematics, or if one is interested in the subject matter, it is a recommendable book. ... Read more

Book Description

This collection of papers is an outgrowth of the `Game Practice I' conference. The overall content of this book is firmly rooted in existing game theory.Much experimental and observational evidence demonstrates that there is a large gap between theory and `practice'. There is no doubt that theory is nonetheless needed, and that it has to be developed. At the same time there is a risk of sterile developments if theory is not fed by challenges coming from confronting the real world. In this respect, the editors' feelings are that there is now a need for a better balance between theory and applications. The kind of considerations sketched above gave birth to the idea of organizing a series of meetings to stimulate research in game theory which seeks a more direct connection with real world problems.Most of the contributions can be roughly classified into four groups: political applications, problems of cost/reward sharing, economic applications, and experiments. The collection is relevant to academics working in game theory and related topics such as management, decision theory and industrial organization. ... Read more

Book Description

This book provides an introduction to the mathematical theory of optimization. It emphasizes the convergence theory of nonlinear optimization algorithms and applications of nonlinear optimization to combinatorial optimization. It includes recent developments in global convergence, the Powell conjecture, semidefinite programming, and relaxation techniques for designs of approximation solutions of combinatorial optimization problems.Audience: The book can be a textbook or useful reference for undergraduate and graduate students in applied mathematics, operations research, and computer science. ... Read more

Book Description

Merging logic and mathematics in deductive inference-an innovative, cutting-edge approach.

Optimization methods for logical inference? Absolutely, say Vijay Chandru and John Hooker, two major contributors to this rapidly expanding field. And even though "solving logical inference problems with optimization methods may seem a bit like eating sauerkraut with chopsticks. . . it is the mathematical structure of a problem that determines whether an optimization model can help solve it, not the context in which the problem occurs."

Presenting powerful, proven optimization techniques for logic inference problems, Chandru and Hooker show how optimization models can be used not only to solve problems in artificial intelligence and mathematical programming, but also have tremendous application in complex systems in general. They survey most of the recent research from the past decade in logic/optimization interfaces, incorporate some of their own results, and emphasize the types of logic most receptive to optimization methods-propositional logic, first order predicate logic, probabilistic and related logics, logics that combine evidence such as Dempster-Shafer theory, rule systems with confidence factors, and constraint logic programming systems.

Requiring no background in logic and clearly explaining all topics from the ground up, Optimization Methods for Logical Inference is an invaluable guide for scientists and students in diverse fields, including operations research, computer science, artificial intelligence, decision support systems, and engineering. ... Read more

Book Description

This volume contains a collection of papers from experts in the field of complementarity on state-of-the-art applications, algorithms, extensions and theory, resulting in a contemporary view of the complete field of complementarity.

The impact of complementarity in such diverse fields as deregulation of electricity markets, engineering mechanics, optimal control and asset pricing is described using both survey and current research articles. The papers outline problem classes where complementarity can be used to model both physical and structural phenomena in ways that lead to new solution approaches. The novel application of complementarity and optimization ideas to problems in the burgeoning fields of machine learning and data mining is covered.New algorithmic advances including preprocessing and nonmonotone searches, extensions of computational methods using tools from nonsmooth analysis, and related theory for mathematical programs with equilibrium constraints is also detailed.

Audience: Researchers and advanced students working in optimization and management sciences. ... Read more