The significant progress that has been made in recent years both in hardware implementations and in numerical computing has rendered real-time optimization-based control a viable option when it comes to advanced industrial applications. More recently, the need for control of a process in the presence of a limited amount of hardware resources has triggered research in the direction of embedded optimization-based control. Operator Splitting Methods in Control focuses on systems with linear dynamics, giving rise to convex control problems. It provides a comprehensive survey of a family of first order methods known as decomposition schemes or operator splitting methods and shows the behavior of such algorithms as solvers of control related convex problems from tens to a few hundreds of variables. This compact survey gives the reader a state-of-the-art overview of the topic with examples of applications in aerospace and building control.

This book studies the methods for solving non-linear, partial differential equations that have physical meaning, and soliton theory with applications. Specific descriptions on the formation mechanism of soliton solutions of non-linear, partial differential equations are given, and some methods for solving this kind of solution such as the Inverse Scattering Transform method, Backlund Transformation method, Similarity Reduction method and several kinds of function transformation methods are introduced. Integrability of non-linear, partial differential equations is also discussed. This book is suitable for graduate students whose research fields are in applied mathematics, applied physics and non-linear science-related directions as a textbook or a research reference book. This book is also useful for non-linear science researchers and teachers as a reference book. The characteristics of this book are: 1. The author provides clear concepts, rigorous derivation, thorough reasoning, and rigorous logic in the book. Since the research boom of non-linear, partial differential equations was rising in the 1960s, the research on non-linear, partial differential equations and soliton theory has only been several decades, which can be described as a very young discipline compared to the other branches in mathematics. Although there are a few related books, they are mostly in highly specialised interdisciplinary areas. There is no book which is suitable for cross-disciplines and for people with college level mathematics and college physics background. This book fills that gap; 2. The book is easy to be understood by readers since it provides step-by-step approaches. All results in the book have been deduced and collated by the author to make sure that they are correct and perfect; 3. The derivation from the physical models to mathematical models is emphasised in the book. In mathematical physics, we cannot just simply consider the mathematical problems without a physical image, which often plays the key role for understanding the mathematical problems; 4. Mathematical transformation methods are provided. The basic idea of various methods for solving non-linear, partial differential equations is to simplify the complex equations into simple ones through some transformations or decompositions. However, we cannot find any patterns for using such transformations or decompositions, and certain conjectures and assumptions have to be used. However, the skill and the logic of using the transformations and decompositions are very important to researchers in this field.

Linear programming (LP), as a specific case of mathematical programming, has been widely encountered in a broad class of scientific disciplines and engineering applications. In view of its fundamental role, the solution of LP has been investigated extensively for the past decades. Due to the parallel-distributed processing nature and circuit-implementation convenience, the neurodynamic solvers based on recurrent neural network (RNN) have been regarded as powerful alternatives to online computation. This book discusses how linear programming is used to plan and schedule the workforce in an emergency room; the neurodynamic solvers, robotic applications, and solution non-uniqueness of linear programming; the mathematical equivalence of simple recourse and chance constraints in linear stochastic programming; and provides a decomposable linear programming model for energy supply chains.

2013 Reprint of 1958 Edition. Full facsimile of the original edition, not reproduced with Optical Recognition Software. A series of lectures on the role of nonlinear processes in physics, mathematics, electrical engineering, physiology, and communication theory. From the preface: "For some time I have been interested in a group of phenomena depending upon random processes. One the one hand, I have recorded the random shot effect as a suitable input for testing nonlinear circuits. On the other hand, for some of the work that Professor W. A. Rosenblith and I have been doing concerning the nature of the electroencephalogram, and in particular of the alpha rhythm, it has occurred to me to use the model of a system of random nonlinear oscillators excited by a random input. . . . At the beginning we had contemplated a series of only four or five lectures. My ideas developed pari passu with the course, and by the end of the term we found ourselves with a set of fifteen lectures. The last few of these were devoted to the application of my ideas to problems in the statistical mechanics of gases. This work is both new and tentative, and I found that I had to supplement my course by the writing over of these with the help of Professer Y. W. Lee. "

This self-contained book provides the reader with a comprehensive presentation of recent investigations on operator theory over non-Archimedean Banach and Hilbert spaces. This includes, non-archimedean valued fields, bounded and unbounded linear operators, bilinear forms, functions of linear operators and one-paramter families of bounded linear operators on free branch spaces.

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.

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.

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.

* What is the essence of the similarity between linearly independent sets of columns of a matrix and forests in a graph?
* Why does the greedy algorithm produce a spanning tree of minimum weight in a connected graph?
* Can we test in polynomial time whether a matrix is totally unimodular?
Matroid theory examines and answers questions like these. Seventy-five years of study of matroids has seen the development of a rich theory with links to graphs, lattices, codes, transversals, and projective geometries. Matroids are of fundamental importance in combinatorial optimization and their applications extend into electrical and structural engineering.
This book falls into two parts: the first provides a comprehensive introduction to the basics of matroid theory, while the second treats more advanced topics. The book contains over seven hundred exercises and includes, for the first time in one place, proofs of all of the major theorems in the subject. The last two chapters review current research and list more than eighty unsolved problems along with a description of the progress towards their solutions.
Reviews from previous edition:
"It includes more background, such as finite fields and finite projective and affine geometries, and the level of the exercises is well suited to graduate students. The book is well written and includes a couple of nice touches ... this is a very useful book. I recommend it highly both as an introduction to matroid theory and as a reference work for those already seriously interested in the subject, whether for its own sake or for its applications to other fields." -- AMS Bulletin
"Whoever wants to know what is happening in one of the most exciting chapters of combinatorics has no choice but to buy and peruse Oxley's treatise." -- The Bulletin of Mathematics
"This book is an excellent graduate textbook and reference book on matroid theory. The care that went into the writing of this book is evident by the quality of the exposition." -- Mathematical Reviews

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.

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."