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.

The goal of this book is to present the main ideas and techniques in the field of continuous smooth and nonsmooth optimization. Starting with the case of differentiable data and the classical results on constrained optimization problems, and continuing with the topic of nonsmooth objects involved in optimization theory, the book concentrates on both theoretical and practical aspects of this field. This book prepares those who are engaged in research by giving repeated insights into ideas that are subsequently dealt with and illustrated in detail.

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. "

Mechanism design is an analytical framework for thinking clearly and carefully about what exactly a given institution can achieve when the information necessary to make decisions is dispersed and privately held. This analysis provides an account of the underlying mathematics of mechanism design based on linear programming. Three advantages characterize the approach. The first is simplicity: arguments based on linear programming are both elementary and transparent. The second is unity: the machinery of linear programming provides a way to unify results from disparate areas of mechanism design. The third is reach: the technique offers the ability to solve problems that appear to be beyond solutions offered by traditional methods. No claim is made that the approach advocated should supplant traditional mathematical machinery. Rather, the approach represents an addition to the tools of the economic theorist who proposes to understand economic phenomena through the lens of mechanism design.

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.

The chapters of this Handbook volume covers nine main topics that are representative of recent
theoretical and algorithmic developments in the field. In addition to the nine papers that present the state of the art, there is an article on
the early history of the field.

The handbook will be a useful reference to experts in the field as well as students and others who want to learn about discrete optimization.

All of the chapters in this handbook are written by authors who have made significant original contributions to their topics. Herewith a brief introduction to the chapters of the handbook.

"On the history of combinatorial optimization (until 1960)" goes back to work of Monge in the 18th century on the assignment problem and presents six problem areas: assignment, transportation,
maximum flow, shortest tree, shortest path and traveling salesman.

The branch-and-cut algorithm of integer programming is the computational workhorse of discrete optimization. It provides the tools that have been implemented in commercial software such as CPLEX
and Xpress MP that make it possible to solve practical problems in supply chain, manufacturing, telecommunications and many other areas.
"Computational integer programming and cutting planes" presents the key ingredients
of these algorithms.

Although branch-and-cut based on linear programming relaxation is the most widely used integer programming algorithm, other approaches are
needed to solve instances for which branch-and-cut performs poorly and to understand better the structure of integral polyhedra. The next three chapters discuss alternative approaches.

"The structure of grouprelaxations" studies a family of polyhedra obtained by dropping certain
nonnegativity restrictions on integer programming problems.

Although integer programming is NP-hard in general, it is polynomially solvable in fixed dimension. "Integer programming, lattices, and results in fixed dimension" presents results in this area including algorithms that use reduced bases of integer lattices that are capable of solving certain classes of integer programs that defy solution by branch-and-cut.

Relaxation or dual methods, such as cutting plane algorithms, progressively remove infeasibility while maintaining optimality to the relaxed problem. Such algorithms have the disadvantage of
possibly obtaining feasibility only when the algorithm terminates.Primal methods for integer programs, which move from a feasible solution to a better feasible solution, were studied in the 1960's
but did not appear to be competitive with dual methods. However, recent development in primal methods presented in "Primal integer programming" indicate that this approach is not just interesting theoretically but may have practical implications as well.

The study of matrices that yield integral polyhedra has a long tradition in integer programming. A major breakthrough occurred in the 1990's with the development of polyhedral and structural results
and recognition algorithms for balanced matrices. "Balanced matrices" is a tutorial on the
subject.

Submodular function minimization generalizes some linear combinatorial optimization problems such as minimum cut and is one of the fundamental problems of the field that is solvable in polynomial
time. "Submodular function minimization"presents the theory and algorithms of this subject.

In the search for tighter relaxations of combinatorial optimization problems, semidefinite programming provides a generalization of
linear programming that can give better approximations and is still polynomially solvable. This subject is discussed in "Semidefinite programming and integer programming,"

Many real world problems have uncertain data that is known only probabilistically. Stochastic programming treats this topic, but until recently it was limited, for computational reasons, to
stochastic linear programs. Stochastic integer programming is now a high profile research area and recent developments are presented in
"Algorithms for stochastic mixed-integer programming
models,"

Resource constrained scheduling is an example of a class of combinatorial optimization problems that is not naturally formulated with linear constraints so that linear programming based methods do
not work well. "Constraint programming" presents an alternative enumerative approach that is complementary to branch-and-cut. Constraint programming, primarily designed for feasibility problems, does not use a relaxation to obtain bounds. Instead nodes of the search tree are
pruned by constraint propagation, which tightens bounds on variables until their values are fixed or their domains are shown to be empty.

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.

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.

Das Buch gibt eine Einfuhrung in das neue Gebiet der Analyse und Optimierung von Tragwerken unter stochastischer Unsicherheit. Es werden die Grundlagen ausfuhrlich dargestellt und zum Teil von unterschiedlichen Standpunkten aus beleuchtet.

In Teil I wird die lineare Theorie der Stabtragwerke als Grundlage fur die FEM entwickelt. Vorausgesetzt werden dabei nur wenige Kenntnisse aus der Technischen Mechanik und der Ingenieurmathematik, insbesondere eine gewisse Vertrautheit mit der Matrizenrechnung.

In Teil II wird dargestellt, wie sich die Wahrscheinlichkeitsverteilungen der Verschiebungen und Spannungen in den Knoten aus denen der stochastischen Stabparameter und ausseren Lasten - zumindest approximativ - berechnen lassen.

In Teil III schliesslich wird die Optimierung von Tragwerken mit stochastischen Parametern behandelt. Dazu wird ein geeignetes deterministisches Ersatzproblem des Ausgangsproblems mit stochastischen Modellparametern formuliert.

Eine kurze Beschreibung einiger Optimierungsverfahren findet man im letzten Abschnitt. Besondere Muhe wurde auf die zahlreichen und eingehend behandelten Beispiele verwandt.

Das Buch ist geschrieben fur Studierende, praktisch tatige Ingenieure und Mathematiker. "

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.

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."

Numerical Linear Algebra and Optimization covers the fundamentals of closely related topics: linear systems (linear equations and least-squares) and linear programming (optimizing a linear function subject to linear constraints). For each problem class, stable and efficient numerical algorithms intended for a finite-precision environment are derived and analyzed. In 1991, when the book first appeared, these topics were rarely taught with a unified perspective, and, somewhat surprisingly, this remains true almost 30 years later. As a result, some of the material in this book can be difficult to find elsewhere-in particular, techniques for updating the LU factorization, descriptions of the simplex method applied to all-inequality form, and the analysis of what happens when using an approximate inverse to solve Ax=b. This book is appropriate for students who want to learn about numerical techniques for solving linear systems and/or linear programming using the simplex method.

Written in a conversational tone, this classroom-tested text introduces the fundamentals of linear programming and game theory, showing readers how to apply serious mathematics to practical real-life questions by modelling linear optimization problems and strategic games. The treatment of linear programming includes two distinct graphical methods. The game theory chapters include a novel proof of the minimax theorem for 2x2 zero-sum games. In addition to zero-sum games, the text presents variable-sum games, ordinal games, and n-player games as the natural result of relaxing or modifying the assumptions of zero-sum games. All concepts and techniques are derived from motivating examples, building in complexity, which encourages students to think creatively and leads them to understand how the mathematics is applied. With no prerequisite besides high school algebra, the text will be useful to motivated high school students and undergraduates studying business, economics, mathematics, and the social sciences.

Compressed sensing is a relatively recent area of research that refers to the recovery of high-dimensional but low-complexity objects from a limited number of measurements. The topic has applications to signal/image processing and computer algorithms, and it draws from a variety of mathematical techniques such as graph theory, probability theory, linear algebra, and optimization. The author presents significant concepts never before discussed as well as new advances in the theory, providing an in-depth initiation to the field of compressed sensing. An Introduction to Compressed Sensing contains substantial material on graph theory and the design of binary measurement matrices, which is missing in recent texts despite being poised to play a key role in the future of compressed sensing theory. It also covers several new developments in the field and is the only book to thoroughly study the problem of matrix recovery. The book supplies relevant results alongside their proofs in a compact and streamlined presentation that is easy to navigate. The core audience for this book is engineers, computer scientists, and statisticians who are interested in compressed sensing. Professionals working in image processing, speech processing, or seismic signal processing will also find the book of interest.