Book Description

Recurrence sequences are of great intrinsic interest and havebeen a central part of number theory for many years. Moreover,these sequences appear almost everywhere in mathematics andcomputer science. This book surveys the modern theory of linearrecurrence sequences and their generalizations. Particularemphasis is placed on the dramatic impact that sophisticatedmethods from Diophantine analysis and transcendence theory havehad on the subject. Related work on bilinear recurrences and anemerging connection between recurrences and graph theory arecovered. Applications and links to other areas of mathematicsare described, including combinatorics, dynamical systems andcryptography, and computer science. The book is suitable forresearchers interested in number theory, combinatorics, andgraph theory. ... Read more

Book Description

Decision makers in many areas, from industry to engineering and the social sector, face an increasing need to consider multiple, conflicting objectives in their decision processes. In many cases these real world decision problems can be formulated as multicriteria mathematical optimization models. The solution of such models requires appropriate techniques to compute so called efficient, or Pareto optimal, or compromise solutions that - unlike traditional mathematical programming methods - take the contradictory nature of the criteria into account. This book provides the necessary mathematical foundation of multicriteria optimization to solve nonlinear, linear and combinatorial problems with multiple criteria. Motivational examples illustrate the use of multicriteria optimization in practice. Numerous illustrations and exercises as well as an extensive bibliography are provided.

In the new edition a chapter on optimality conditions has been added. The linear programming part has been extended and includes new developments. Moreover, motivational examples are now introducing the majority of chapters.

Book Description

Revisiting classical theory within the context of contemporary results, this authoritative volume presents cutting-edge research contributions and tutorial expositions on current methodologies for sensitivity, stability, and approximation analyses of mathematical programming and related problem structures involving parameters.Mathematical Programming with Data Perturbations features the latest findings on important topics, coveringthe effect of perturbations on the performance of algorithmsapproximation techniques for optimal control problemsglobal error bounds for convex inequalitieswell-posedness by perturbationsweak second-order conditions and attendant first- and second-order differential stability resultsstability characterizations of the parametric linear complementarity solution set maprelations between complexity bounds and parameter structuresecond-order sufficient conditions for weak sharp minima and more!Containing key references to the literature, Mathematical Programming with Data Perturbations is a valuable resource for applied mathematicians, mathematical programmers, researchers in optimization and stability analysis, operations researchers, economists, engineers, and graduate-level students in these disciplines. ... Read more

Book Description

Growing transportation costs and tight delivery schedules mean that good located decisions are more crucial than ever in the success or failure of industrial and puplic projects. The development of realistic location models is an essential phase in every locational decision process. Especially when dealing with geometric representations of continuous (planar) location model problems, the goegraphical reality must be incorporated. This text develops the mathematical implications of barriers to the geometrical and analytical characteristics of continuous location problems. Besides their relevance in the application of location theoretic results, location problems with barriers are also very interesting from a mathematical point of view. The nonconvexity of distance measures in the presence of barriers leads to nonconvex optimization problems. Most of the classical methods in continuous location theory rely heaily on the convexity of the objective function and will thus fail in this context. On the other hand, general methods in global optimization capable of treating nonconvex problems ignore the geometric charateristics of the location problems considered. Theoretic as well as algorithmic approaches are utilized to overcome the described difficulties for the solution of location problems with barriers. Depending on the barrier shapes, the underlying distance measure, and type of objective function, different concepts are conceived to handle the nonconvexity of the problem.

This book will appeal to those working in operations research and management science and mathematicians interested in optimization theory and its applications. ... Read more

Book Description

The Sixth Workshop on Optimization and Numerical Analysis washeld in Oaxaca, Mexico, in January 1992. The participation of many of the leading figures in the field resultedin this excellent state of the art volume on continuous optimization.The papers presented here give a good overview of several topicsincluding interior point and simplex methods for linear programmingproblems, new methods for nonlinear programming, results in non-convexlinear complementarity problems and non-smooth optimization. There areseveral articles dealing with the numerical solution ofdiffusion--advection equations. For researchers and postgraduate students in optimization, partialdifferential equations and modelling. ... Read more

Book Description

This volume provides a compilation of recent contributions on feedback and robust control, modeling, estimation and filtering. They were presented on the occasion of the sixtieth birthday of Anders Lindquist, who has delivered fundamental contributions to the fields of systems, signals and control for more than three decades. His contributions include seminal work on the role of splitting subspaces in stochastic realization theory, on the partial realization problem for both deterministic and stochastic systems, on the solution of the rational covariance extension problem and on system identification. Lindquist's research includes the development of fast filtering algorithms, leading to a nonlinear dynamical system which computes spectral factors in its steady state, and which provide an alternate, linear in the dimension of the state space, to computing the Kalman gain from a matrix Riccati equation. He established the separation principle for stochastic function differential equations, including some fundamental work on optimal control for stochastic systems with time lags. His recent work on a complete parameterization of all rational solutions to the Nevanlinna-Pick problem is providing a new approach to robust control design. ... Read more

Book Description

In science, engineering and economics, decision problems are frequently modelled by optimizing the value of a (primary) objective function under stated feasibility constraints. In many cases of practical relevance, the optimization problem structure does not warrant the global optimality of local solutions; hence, it is natural to search for the globally best solution(s).Global Optimization in Action provides a comprehensive discussion of adaptive partition strategies to solve global optimization problems under very general structural requirements. A unified approach to numerous known algorithms makes possible straightforward generalizations and extensions, leading to efficient computer-based implementations. A considerable part of the book is devoted to applications, including some generic problems from numerical analysis, and several case studies in environmental systems analysis and management. The book is essentially self-contained and is based on the author's research, in cooperation (on applications) with a number of colleagues.Audience: Professors, students, researchers and other professionals in the fields of operations research, management science, industrial and applied mathematics, computer science, engineering, economics and the environmental sciences. ... Read more

Book Description

This book includes a collection of articles that present recent developments in the fields of optimization and dynamic game theory, economic dynamics, dynamic theory of the firm, and population dynamics and non standard applications of optimal control theory. The authors of the articles are well respected authorities in their fields and are known for their high quality research in the fields of optimization and economic dynamics. ... Read more

Book Description

The effectiveness of the algorithms of linear programming in solving problems is largely dependent upon the particular applications from which these problems arise. A first course in linear programming should not only allow one to solve many different types of problems in many different contexts but should provide deeper insights into the fields in which linear programming finds its utility. To this end, the emphasis throughtout Linear Programming and Its Applications is on the acquisition of linear programming skills via the algorithmic solution of small-scale problems both in the general sense and in the specific applications where these problems naturally occur. The first part of the book deals with methods to solve general linear programming problems and discusses the theory of duality which connects these problems. The second part of the book deals with linear programming in different applications including the fields of game theory and graph theory as well as the more traditional transportation and assignment problems. The book is versatile; in as much as Linear Programming and Its Applications is intended to be used as a first course in linear programming, it is suitable for students in such varying fields as mathematics, computer science, engineering, actuarial science, and economics. ... Read more

Reviews (1)

highly erudite
I took the class for which this book was used as a sophomore, and found it to be very accessible. In retrospect, I would have liked to have studied some linear algebra before having taken this course, but still, I found this to be a very interesting course as a stand-alone. ... Read more

Book Description

This book is unique in that it presents a profound mathematical analysis of general optimization problems for elliptic systems, which are then applied to a great number of optimization problems in mechanics and technology. After the setting of a problem, attention is focused on existence theorems that lead to the construction of approximate solutions. The coefficients of the equations, the shape of the domain, and the right-hand sides of the equations are considered to be controls. Applications include optimization problems arising in mechanics of elastic solids, plates, shells, composite materials and structures fabricated with them, as well as fluid mechanics.The monograph is written in an accessible and self-contained manner. It will be of interest to research mathematicians and science engineers working in solid and fluid mechanics, and in optimization theory of partial differential equations. Moreover, it is suitable as a textbook for graduate courses in optimization of elliptic systems. ... Read more

Book Description

This textbook provides an introduction to the new science of nonlinear physics for advanced undergraduates, beginning graduate students, and researchers entering the field. The chapters, by pioneers and experts in the field, share a unified perspective. Nonlinear science developed out of the increasing ability to investigate and analyze systems for which effects are not simply linear functions of their causes; it is associated with such well-known code words as chaos, fractals, pattern formation, solitons, cellular automata, and complex systems. Nonlinear phenomena are important in many fields, including dynamical systems, fluid dynamics, materials science, statistical physics, and paritcel physics. The general principles developed in this text are applicable in a wide variety of fields in the natural and social sciences. The book will thus be of interest not only to physicists, but also to engineers, chemists, geologists, biologists, economists, and others interested in nonlinear phenomena. Examples and exercises complement the text, and extensive references provide a guide to research in the field. ... Read more

Book Description

In 1984, N. Karmarkar published a seminal paper on algorithmic linear programming. During the subsequent decade, it stimulated a huge outpouring of new algorithmic results by researchers world-wide in many areas of mathematical programming and numerical computation. This book gives an overview of the resulting, dramatic reorganization that has occurred in one of these areas: algorithmic differentiable optimization and equation-solving, or, more simply, algorithmic differentiable programming. The book is aimed at readers familiar with advanced calculus, numerical analysis, in particular numerical linear algebra, the theory and algorithms of linear and nonlinear programming, and the fundamentals of computer science, in particular, computer programming and the basic models of computation and complexity theory.

J.L. Nazareth is a Professor in the Department of Pure and Applied Mathematics at Washington State University. He is the author of two books previously published by Springer-Verlag, DLP and Extensions: An Optimization Model and Decision Support System (2001) and The Newton-Cauchy Framework: A Unified Approach to Unconstrained Nonlinear Minimization (1994). ... Read more

Book Description

This volume is a collection of recent key results in supply chain optimisation. It presents new approaches and methods based on operations research, artificial intelligence and computer sciences techniques for design of production systems, supply and inventory management, production planning and scheduling, facility location, transportation and logistics, supply flow optimisation via simulation, etc. The content focuses on a wide spectrum of optimisation problems taking into account supply chain paradigms, which create a pivotal idea to increase the productivity of modern production systems.

Book Description

Carefully written to cover all necessary background material from both linear and non-linear programming as well as probability theory, the book brings together the methods and techniques previously described in disparate sources. Topics include decision trees and dynamic programming, recourse problems, probabilistic constraints, preprocessing and network problems. Emphasises the appropriate use of the techniques described. Exercises are provided at the end of each chapter. ... Read more

Reviews (1)

GOOD BOOK : GOOD NEWS
I higghly recommend this book for a starting point in Stochastic optimization. It is
perfectly suitable for a person with no background in this field. The best part is
Wiley has released the copyright on the book, and the authors made the text available to the scientific community: it can be downloaded for free. Folllow the link at the Stochastic Programming Community Home page (SP resources-Textbooks). ... Read more