Linear programming finds the least expensive way to meet given needs with available resources. Its results are used in every area of engineering and commerce: agriculture, oil refining, banking, and air transport. Authors Kolman and Beck present the basic notions of linear programming and illustrate how they are used to solve important common problems. The software on the included disk leads students step-by-step through the calculations. The Second Edition is completely revised and provides additional review material on linear algebra as well as complete coverage of elementary linear programming. Other topics covered include: the Duality Theorem; transportation problems; the assignment problem; and the maximal flow problem. New figures and exercises are provided and the authors have updated all computer applications. Thecompanion website on www.elsevierdirect.comcontains the student-oriented linear programming code SMPX, written by Professor Evar Nering of Arizona State University. The authors also recommend inexpensive linear programming software for personal computers.

Please note the previous printing included a disk attached to the back of the book.

The material is now only available on the companion website -

http: //www.elsevierdirect.com/product.jsp?isbn=9780124179103

* More review material on linear algebra * Elementary linear programming covered more efficiently * Presentation improved, especially for the duality theorem, transportation problems, the assignment problem, and the maximal flow problem * New figures and exercises * Computer applications updated * Companion website on www.elsevierdirect.com with the student-oriented linear programming code SMPX, written by Professor Evar Nering of Arizona State University * New guide to inexpensive linear programming software for personal computers

Please note the previous printing included a disk attached to the back of the book.

The material is now only available on the companion website -

http: //www.elsevierdirect.com/product.jsp?isbn=9780124179103"

Das Buch gibt eine Einfuhrung in zentrale Konzepte und Methoden der Nichtlinearen Optimierung. Es ist aus Vorlesungen der Autoren an der TU Munchen, der TU Darmstadt und der Universitat Hamburg entstanden. Der Inhalt des Buches wurde insbesondere auf mathematische Bachelorstudiengange zugeschnitten und hat sich als Basis entsprechender Vorlesungen sowie fur eine anschlieende Vertiefung im Bereich der Optimierung bewahrt. Der Umfang entspricht zwei zweistundigen oder einer vierstundigen Vorlesung, wobei etwa in gleichem Umfang sowohl unrestringierte Optimierungsprobleme als auch Optimierungsprobleme mit Nebenbedingungen behandelt werden. Im Teil uber die unrestringierte Optimierung werden sowohl Trust-Region- als auch Liniensuch-Methoden zur Globalisierung behandelt. Fur letztere wird ein ebenso leistungsfahiges wie intuitives Konzept der zulassigen Suchrichtungen und Schrittweiten entwickelt. Die schnelle lokale Konvergenz Newton-artiger Verfahren und ihre Globalisierung sind weitere wichtige Themengebiete. Das Kapitel uber restringierte Optimierung entwickelt notwendige und hinreichende Optimalitatsbedingungen und geht auf wichtige numerische Verfahren, insbesondere Sequential Quadratic Programming, Penalty- und Barriereverfahren ein. Der Bezug von Barriereverfahren zu den aktuell intensiv untersuchten Innere-Punkte-Verfahren wird ebenfalls hergestellt.

La proposta nasce dalla constatazione dell'importanza dell'approccio quantitativo a problemi di rilevanza quotidiana in molte realta industriali. L'opera, oltre a proporre modelli di riferimento, vuole promuovere la comprensione degli stessi e degli approcci formali ad essi collegati attraverso costanti riferimenti a reali pratiche di pianificazione e gestione. Il panorama editoriale italiano non sembra offrire nell'ambito del business management un'opera avente questo stesso indirizzo. L'esperienza acquisita dagli autori nei rapporti professionali con diverse realta industriali e alla base della qualita complessiva dell'opera. Gli obiettivi principali sono: presentare modelli di ottimizzazione tratti o ispirati da casi di studio concreti nell'ambito industriale, manifatturiero e logistico; illustrare alcuni dei principali approcci di modellazione matematica ai problemi di rilevanza industriale; costituire materiale didattico integrativo per corsi a livello universitario ed avanzato.

a žAlle Wege fA1/4hren nach Rom!" Aber welcher ist der beste a " wie findet mein Navi den Weg A1/4berhaupt? Und was ist mit einer Rundreise durch Europas HauptstAdte?

Diese Fragen bilden nur einen kleinen Teilaspekt der Themen dieses Buches. Anhand vieler Praxissituationen werden die Begriffe der Graphentheorie und Netzwerkoptimierung eingefA1/4hrt und die aufgeworfenen Probleme anschlieAend mit Hilfe von Algorithmen gelAst.

Das Buch richtet sich an Studierende der Mathematik und Informatik in den ersten Semestern sowie an interessierte Praktiker. Es enthAlt eine Vielzahl an Anwendungsbeispielen sowie wichtige in der Praxis relevanten Algorithmen mit dem Beweis ihrer OptimalitAt.

Spezielle mathematische Vorkenntnisse sind nicht erforderlich: SAmtliche Begriffe und Methoden werden auf verstAndliche Weise eingefA1/4hrt. Das so erworbene Wissen kann anhand zahlreicher Aoebungsaufgaben und deren LAsungen vertieft und A1/4berprA1/4ft werden.

L'objectif et l'originalite de ce livre est de presenter les differents aspects et methodes utilises dans la resolution des problemes d'optimisation stochastique avec en vue des applications plus specifiques a la finance: gestion de portefeuille, couverture d'options, investissement optimal.
Nous avons inclus certains developpements recents sur le sujet sans chercher a priori la plus grande generalite. Nous avons voulu une exposition graduelle des methodes mathematiques en presentant d'abord les idees intuitives puis en enoncant precisement les resultats avec des demonstrations completes et detaillees.
Nous avons aussi pris soin d'illustrer chacune des methodes de resolution sur de
nombreux exemples issus de la finance. Nous esperons ainsi que ce livre puisse etre utile aussi bien pour des etudiants que pour des chercheurs du monde academique ou professionnel interesses par l'optimisation et le controle stochastique appliques a la finance.

Les buts principaux de cet ouvrage qui comble un vide sont de:

- donner les concepts et r sultats fondamentaux sur les ensembles ordonn?'s finis,

- pr senter leurs usages dans des domaines vari?'s (de la RO ou l IA la micro- conomie),

- signaler un certain nombre de r sultats et de recherches en cours.

The aim of this book is two-fold: to introduce the fundamental concepts of linear algebra and to apply the theorems in computation-oriented applications. The book is suitable for a one semester course in linear algebra that can be used in a variety of contexts. The presentation of the material combines definitions and proofs with an emphasis on computational applications, providing examples that illustrate the use of software packages such as Mathematica (R),Maple (R), and Sage. Features: Introduces the fundamental concepts of linear algebra and applies the theorems in computation-oriented applications Presents a brief introduction of some aspects of abstract algebra that relate directly to linear algebra, such as groups, rings, modules, fields and polynomials over fields.

In the past decade, primal-dual algorithms have emerged as the most important and useful algorithms from the interior-point class. This book presents the major primal-dual algorithms for linear programming in straightforward terms. A thorough description of the theoretical properties of these methods is given, as are a discussion of practical and computational aspects and a summary of current software. This is an excellent, timely, and well-written work. The major primal-dual algorithms covered in this book are path-following algorithms (short- and long-step, predictor-corrector), potential-reduction algorithms, and infeasible-interior-point algorithms. A unified treatment of superlinear convergence, finite termination, and detection of infeasible problems is presented. Issues relevant to practical implementation are also discussed, including sparse linear algebra and a complete specification of Mehrotra's predictor-corrector algorithm. Also treated are extensions of primal-dual algorithms to more general problems such as monotone complementarity, semidefinite programming, and general convex programming problems.

Conception optimale des structures est une introduction a la conception optimale de structures, appelee aussi optimisation de formes. Il est principalement destine a un public mixte de mathematiciens appliques et de mecaniciens que relient un meme interet pour les applications numeriques."

La publicacion no es unicamente un libro de ejercicios resueltos de programacion lineal para estudiantes, sino una fuente de informacion e incluso, en cierto modo, puede hablarse de una metodologia para la resolucion de dichos ejercicios, de interes tanto para estudiantes como para profesionales que en su trabajo lleven a cabo actividades de optimizacion tanto en el ambito de la empresa privada como en las administraciones publicas. Ha sido planificado para su utilizacion por personas con conocimientos de programacion lineal, primordialmente para facilitar el aprendizaje de los conceptos y procedimientos de formulacion y resolucion de modelos de programacion lineal de los estudiantes de dicha materia en las diversas Facultades y Escuelas Tecnicas en las que se imparte. Su finalidad es eminentemente didactica, y unicamente por razones pedagogicas se justifica la presente publicacion.

Presenting recent developments of key topics in nonlinear programming, this text looks specifically at three main areas; convex analysis, optimality conditions and dual computational techniques.

A comprehensive and rigorous introduction to optimization and approximation, including many exercises and examples.

No one working in duality should be without a copy of Convex Analysis and Variational Problems. This book contains different developments of infinite dimensional convex programming in the context of convex analysis, including duality, minmax and Lagrangians, and convexification of nonconvex optimization problems in the calculus of variations (infinite dimension). It also includes the theory of convex duality applied to partial differential equations; no other reference presents this in a systematic way. The minmax theorems contained in this book have many useful applications, in particular the robust control of partial differential equations in finite time horizon. First published in English in 1976, this SIAM Classics in Applied Mathematics edition contains the original text along with a new preface and some additional references.

Generalized linear models (GLMs) extend linear regression to models with a non-Gaussian, or even discrete, response. GLM theory is predicated on the exponential family of distributions-a class so rich that it includes the commonly used logit, probit, and Poisson models. Although one can fit these models in Stata by using specialized commands (for example, logit for logit models), fitting them as GLMs with Stata's glm command offers some advantages. For example, model diagnostics may be calculated and interpreted similarly regardless of the assumed distribution. This text thoroughly covers GLMs, both theoretically and computationally, with an emphasis on Stata. The theory consists of showing how the various GLMs are special cases of the exponential family, showing general properties of this family of distributions, and showing the derivation of maximum likelihood (ML) estimators and standard errors. Hardin and Hilbe show how iteratively reweighted least squares, another method of parameter estimation, are a consequence of ML estimation using Fisher scoring.

The problem of efficient or optimal allocation of resources is a fundamental concern of economic analysis. The theory of optimal economic growth can be viewed as an aspect of this central theme, which emphasizes in general the issues arising in the allocation of resources over an infinite time horizon, and in particular the consumption-investment decision process in models in which there is no natural "terminal date". This broad scope of "optimal growth theory" is one which has evolved over time, as economists have discovered new interpretations of its central results, as well as new applications of its basic methods. The "Handbook on Optimal Growth" provides surveys of significant results of the theory of optimal growth, as well as the techniques of dynamic optimization theory on which they are based. Armed with the results and methods of this theory, a researcher will be in an advantageous position to apply these versatile methods of analysis to new issues in the area of dynamic economics.

This text is one of the first to treat vector calculus using differential forms in place of vector fields and other outdated techniques. Geared towards students taking courses in multivariable calculus, this innovative book aims to make the subject more readily understandable. Differential forms unify and simplify the subject of multivariable calculus, and students who learn the subject as it is presented in this book should come away with a better conceptual understanding of it than those who learn using conventional methods.

The efficient numerical solution of PDE constrained optimization problems plays an important role in many engineering and science applications. The development of robust and efficient numerical algorithms requires the integration of tools from several mathematical subdisciplines, often only described individually in books or journal articles. The goal of this book is to provide readers with a brief introduction to this active research area as well as with an overview of the state-of-the-art in the important topics of adaptive discretizations of PDE optimization problems, handling of control and state constraints, domain decomposition and homogenization of PDEs on networks, and reduced order modeling.

Performance analysis of modern communication systems has lead to a revision and sharpening of nonlinear stability analysis techniques developed over the last century. Applicability of such techniques involves a number of areas, including: process control systems, active queue management in data networks, and other branches of engineering. This monograph presents some recent performance analysis results within a unified stability analysis framework. Several interesting counterexamples to the existing nonlinear stability theory are given. Additionally, several cutting-edge case studies from air traffic control systems and data networks are presented to further illustrate the applications of the theory. The main theoretical results build upon the well-established multiplier theory, which has received much interest because of recent advances in software packages such as the linear matrix inequality (LMI) toolbox. The exposition demonstrates the existence of monotone nonlinearites in problems of interest and gives an exhaustive stability analysis treatment of systems containing such nonlinearities. Key features: * broad range of topics: stability analysis, monotone nonlinearities, multiplier theory, service quality in data networks, protocol scalability, air traffic congestion control * recent and original results presented * many examples and case studies illustrate the applicability of the theory * comprehensive glossaries, bibliography, index, and appendices "Qualitative Nonlinear Dynamics of Communication Networks" is a useful reference for graduate students, and practitioners in control, computer, electrical, aerospace, and mechanical engineering. It can be used as a supplementary textfor nonlinear stability courses at the graduate level. Prerequisites are a familiarity with elementary control theory, linear systems theory, matrix theory, and functional analysis.