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Books > Science & Mathematics > Mathematics > Optimization > Linear programming

Matroid Theory (Hardcover, 2nd Revised edition): James Oxley Matroid Theory (Hardcover, 2nd Revised edition)
James Oxley
R6,190 Discovery Miles 61 900 Ships in 12 - 17 working days

* 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

Continental Adventures (Paperback): Charlotte Anne Eaton Continental Adventures (Paperback)
Charlotte Anne Eaton
R584 Discovery Miles 5 840 Ships in 12 - 17 working days
Continental Adventures (Paperback): Charlotte Anne Eaton Continental Adventures (Paperback)
Charlotte Anne Eaton
R546 Discovery Miles 5 460 Ships in 12 - 17 working days
Retail Arbitrage - How to Make Money Online with Proven and Powerful Strategies in Today's Market! Create Passive Income... Retail Arbitrage - How to Make Money Online with Proven and Powerful Strategies in Today's Market! Create Passive Income with Amazon FBA, Affiliate Marketing, eBay and E-Commerce! (Hardcover)
Tony Bennis
R737 Discovery Miles 7 370 Ships in 10 - 15 working days
Nonlinear Optimization - Models and Applications (Paperback): William P. Fox Nonlinear Optimization - Models and Applications (Paperback)
William P. Fox
R1,767 Discovery Miles 17 670 Ships in 12 - 17 working days

Optimization is the act of obtaining the "best" result under given circumstances. In design, construction, and maintenance of any engineering system, engineers must make technological and managerial decisions to minimize either the effort or cost required or to maximize benefits. There is no single method available for solving all optimization problems efficiently. Several optimization methods have been developed for different types of problems. The optimum-seeking methods are mathematical programming techniques (specifically, nonlinear programming techniques). Nonlinear Optimization: Models and Applications presents the concepts in several ways to foster understanding. Geometric interpretation: is used to re-enforce the concepts and to foster understanding of the mathematical procedures. The student sees that many problems can be analyzed, and approximate solutions found before analytical solutions techniques are applied. Numerical approximations: early on, the student is exposed to numerical techniques. These numerical procedures are algorithmic and iterative. Worksheets are provided in Excel, MATLAB(R), and Maple(TM) to facilitate the procedure. Algorithms: all algorithms are provided with a step-by-step format. Examples follow the summary to illustrate its use and application. Nonlinear Optimization: Models and Applications: Emphasizes process and interpretation throughout Presents a general classification of optimization problems Addresses situations that lead to models illustrating many types of optimization problems Emphasizes model formulations Addresses a special class of problems that can be solved using only elementary calculus Emphasizes model solution and model sensitivity analysis About the author: William P. Fox is an emeritus professor in the Department of Defense Analysis at the Naval Postgraduate School. He received his Ph.D. at Clemson University and has taught at the United States Military Academy and at Francis Marion University where he was the chair of mathematics. He has written many publications, including over 20 books and over 150 journal articles. Currently, he is an adjunct professor in the Department of Mathematics at the College of William and Mary. He is the emeritus director of both the High School Mathematical Contest in Modeling and the Mathematical Contest in Modeling.

Linear and Nonlinear Programming (Hardcover, 5th ed. 2021): David G. Luenberger, Yinyu Ye Linear and Nonlinear Programming (Hardcover, 5th ed. 2021)
David G. Luenberger, Yinyu Ye
R2,948 R2,040 Discovery Miles 20 400 Save R908 (31%) Ships in 12 - 17 working days

The 5th edition of this classic textbook covers the central concepts of practical optimization techniques, with an emphasis on methods that are both state-of-the-art and popular. One major insight is the connection between the purely analytical character of an optimization problem and the behavior of algorithms used to solve that problem. End-of-chapter exercises are provided for all chapters. The material is organized into three separate parts. Part I offers a self-contained introduction to linear programming. The presentation in this part is fairly conventional, covering the main elements of the underlying theory of linear programming, many of the most effective numerical algorithms, and many of its important special applications. Part II, which is independent of Part I, covers the theory of unconstrained optimization, including both derivations of the appropriate optimality conditions and an introduction to basic algorithms. This part of the book explores the general properties of algorithms and defines various notions of convergence. In turn, Part III extends the concepts developed in the second part to constrained optimization problems. Except for a few isolated sections, this part is also independent of Part I. As such, Parts II and III can easily be used without reading Part I and, in fact, the book has been used in this way at many universities. New to this edition are popular topics in data science and machine learning, such as the Markov Decision Process, Farkas' lemma, convergence speed analysis, duality theories and applications, various first-order methods, stochastic gradient method, mirror-descent method, Frank-Wolf method, ALM/ADMM method, interior trust-region method for non-convex optimization, distributionally robust optimization, online linear programming, semidefinite programming for sensor-network localization, and infeasibility detection for nonlinear optimization.

Discrete Optimization, Volume 11 - The State of the Art (Hardcover, New): E. Boros, P. L Hammer Discrete Optimization, Volume 11 - The State of the Art (Hardcover, New)
E. Boros, P. L Hammer
R2,489 Discovery Miles 24 890 Ships in 12 - 17 working days

One of the most frequently occurring types of optimization problems involves decision variables which have to take integer values. From a practical point of view, such problems occur in countless areas of management, engineering, administration, etc., and include such problems as location of plants or warehouses, scheduling of aircraft, cutting raw materials to prescribed dimensions, design of computer chips, increasing reliability or capacity of networks, etc. This is the class of problems known in the professional literature as "discrete optimization" problems. While these problems are of enormous applicability, they present many challenges from a computational point of view. This volume is an update on the impressive progress achieved by mathematicians, operations researchers, and computer scientists in solving discrete optimization problems of very large sizes. The surveys in this volume present a comprehensive overview of the state of the art in discrete optimization and are written by the most prominent researchers from all over the world.


This volume describes the tremendous progress in discrete optimization achieved in the last 20 years since the publication of Discrete Optimization '77, Annals of Discrete Mathematics, volumes 4 and 5, 1979 (Elsevier). It contains surveys of the state of the art written by the most prominent researchers in the field from all over the world, and covers topics like neighborhood search techniques, lift and project for mixed 0-1 programming, pseudo-Boolean optimization, scheduling and assignment problems, production planning, location, bin packing, cutting planes, vehicle routing, and applications to graph theory, mechanics, chip design, etc.


Key features:
state of the art surveys
comprehensiveness
prominent authors
theoretical, computational and applied aspects.


This book is a reprint of "Discrete Applied Mathematics" Volume 23, Numbers 1-3
"

Relaxation in Optimization Theory and Variational Calculus (Hardcover, 2nd Revised and Extended Edition): Tomas Roubicek Relaxation in Optimization Theory and Variational Calculus (Hardcover, 2nd Revised and Extended Edition)
Tomas Roubicek
R4,364 Discovery Miles 43 640 Ships in 12 - 17 working days

The relaxation method has enjoyed an intensive development during many decades and this new edition of this comprehensive text reflects in particular the main achievements in the past 20 years. Moreover, many further improvements and extensions are included, both in the direction of optimal control and optimal design as well as in numerics and applications in materials science, along with an updated treatment of the abstract parts of the theory.

Computational Linear and Commutative Algebra (Hardcover, 1st ed. 2016): Martin Kreuzer, Lorenzo Robbiano Computational Linear and Commutative Algebra (Hardcover, 1st ed. 2016)
Martin Kreuzer, Lorenzo Robbiano
R2,528 Discovery Miles 25 280 Ships in 12 - 17 working days

This book combines, in a novel and general way, an extensive development of the theory of families of commuting matrices with applications to zero-dimensional commutative rings, primary decompositions and polynomial system solving. It integrates the Linear Algebra of the Third Millennium, developed exclusively here, with classical algorithmic and algebraic techniques. Even the experienced reader will be pleasantly surprised to discover new and unexpected aspects in a variety of subjects including eigenvalues and eigenspaces of linear maps, joint eigenspaces of commuting families of endomorphisms, multiplication maps of zero-dimensional affine algebras, computation of primary decompositions and maximal ideals, and solution of polynomial systems. This book completes a trilogy initiated by the uncharacteristically witty books Computational Commutative Algebra 1 and 2 by the same authors. The material treated here is not available in book form, and much of it is not available at all. The authors continue to present it in their lively and humorous style, interspersing core content with funny quotations and tongue-in-cheek explanations.

Linear and Integer Programming Made Easy (Hardcover, 1st ed. 2016): T.C. Hu, Andrew B. Kahng Linear and Integer Programming Made Easy (Hardcover, 1st ed. 2016)
T.C. Hu, Andrew B. Kahng
R2,161 Discovery Miles 21 610 Ships in 12 - 17 working days

This textbook provides concise coverage of the basics of linear and integer programming which, with megatrends toward optimization, machine learning, big data, etc., are becoming fundamental toolkits for data and information science and technology. The authors' approach is accessible to students from almost all fields of engineering, including operations research, statistics, machine learning, control system design, scheduling, formal verification and computer vision. The presentations enables the basis for numerous approaches to solving hard combinatorial optimization problems through randomization and approximation. Readers will learn to cast various problems that may arise in their research as optimization problems, understand the cases where the optimization problem will be linear, choose appropriate solution methods and interpret results appropriately.

Compact Extended Linear Programming Models (Hardcover, 1st ed. 2018): Giuseppe Lancia, Paolo Serafini Compact Extended Linear Programming Models (Hardcover, 1st ed. 2018)
Giuseppe Lancia, Paolo Serafini
R3,055 Discovery Miles 30 550 Ships in 12 - 17 working days

This book provides a handy, unified introduction to the theory of compact extended formulations of exponential-size integer linear programming (ILP) models. Compact extended formulations are equally powerful, but polynomial-sized, models whose solutions do not require the implementation of separation and pricing procedures. The book is written in a general, didactic form, first developing the background theoretical concepts (polyhedra, projections, linear and integer programming) and then delving into the various techniques for compact extended reformulations. The techniques are illustrated through a wealth of examples touching on many application areas, such as classical combinatorial optimization, network design, timetabling, scheduling, routing, computational biology and bioinformatics. The book is intended for graduate or PhD students - either as an advanced course on selected topics or within a more general course on ILP and mathematical programming - as well as for practitioners and software engineers in industry exploring techniques for developing optimization models for their specific problems.

An Economic Interpretation of Linear Programming (Hardcover, 1st ed. 2015): Quirino Paris An Economic Interpretation of Linear Programming (Hardcover, 1st ed. 2015)
Quirino Paris
R3,666 Discovery Miles 36 660 Ships in 12 - 17 working days

This text covers the basic theory and computation for mathematical modeling in linear programming. It provides a strong background on how to set up mathematical proofs and high-level computation methods, and includes substantial background material and direction. Paris presents an intuitive and novel discussion of what it means to solve a system of equations that is a crucial stepping stone for solving any linear program. The discussion of the simplex method for solving linear programs gives an economic interpretation to every step of the simplex algorithm. The text combines in a unique and novel way the microeconomics of production with the structure of linear programming to give students and scholars of economics a clear notion of what it means, formulating a model of economic equilibrium and the computation of opportunity cost in the presence of many outputs and inputs.

Multiobjective Linear Programming - An Introduction (Hardcover, 1st ed. 2016): Dinh The Luc Multiobjective Linear Programming - An Introduction (Hardcover, 1st ed. 2016)
Dinh The Luc
R3,022 Discovery Miles 30 220 Ships in 12 - 17 working days

This book introduces the reader to the field of multiobjective optimization through problems with simple structures, namely those in which the objective function and constraints are linear. Fundamental notions as well as state-of-the-art advances are presented in a comprehensive way and illustrated with the help of numerous examples. Three of the most popular methods for solving multiobjective linear problems are explained, and exercises are provided at the end of each chapter, helping students to grasp and apply key concepts and methods to more complex problems. The book was motivated by the fact that the majority of the practical problems we encounter in management science, engineering or operations research involve conflicting criteria and therefore it is more convenient to formulate them as multicriteria optimization models, the solution concepts and methods of which cannot be treated using traditional mathematical programming approaches.

Advances in Data Analysis - Theory and Applications to Reliability and Inference, Data Mining, Bioinformatics, Lifetime Data,... Advances in Data Analysis - Theory and Applications to Reliability and Inference, Data Mining, Bioinformatics, Lifetime Data, and Neural Networks (Hardcover, 2010 ed.)
Christos H. Skiadas
R5,168 Discovery Miles 51 680 Ships in 12 - 17 working days

This unified volume is a collection of invited chapters presenting recent developments in the field of data analysis, with applications to reliability and inference, data mining, bioinformatics, lifetime data, and neural networks. The book is a useful reference for graduate students, researchers, and practitioners in statistics, mathematics, engineering, economics, social science, bioengineering, and bioscience.

Discrete-Time Linear Systems - Theory and Design with Applications (Hardcover, 2012 ed.): Guoxiang Gu Discrete-Time Linear Systems - Theory and Design with Applications (Hardcover, 2012 ed.)
Guoxiang Gu
R1,602 Discovery Miles 16 020 Ships in 10 - 15 working days

"Discrete-Time Linear Systems: Theory and Design with Applications "combines system theory and design in order to show the importance of system theory and its role in system design. The book focuses on system theory (including optimal state feedback and optimal state estimation) and system design (with applications to feedback control systems and wireless transceivers, plus system identification and channel estimation).

Differential Evolution - In Search of Solutions (Hardcover, 2006 ed.): Vitaliy Feoktistov Differential Evolution - In Search of Solutions (Hardcover, 2006 ed.)
Vitaliy Feoktistov
R1,639 Discovery Miles 16 390 Ships in 10 - 15 working days

This book presents an overview of the differential evolution algorithm. In the last few years the evolutionary computation domain has developed rapidly, and differential evolution is one of the representatives of this domain. It is a recently invented evolutionary algorithm that is gaining more and more popularity. Originally proposed for continuous unconstraint optimization, it was enlarged both for mixed optimization and for handling nonlinear constraints. Later on, new strategies, tuning, and adaptation of control parameters, ways of hybridization were elaborated. Attempts at theoretical analysis were accomplished as well. Moreover, the algorithm has a huge number of practical applications in different areas of science and industry.

Queueing Networks - A Fundamental Approach (Hardcover, 2011 Ed.): Richard J Boucherie, Nico M. van Dijk Queueing Networks - A Fundamental Approach (Hardcover, 2011 Ed.)
Richard J Boucherie, Nico M. van Dijk
R6,060 Discovery Miles 60 600 Ships in 10 - 15 working days

This handbook aims to highlight fundamental, methodological and computational aspects of networks of queues to provide insights and to unify results that can be applied in a more general manner. The handbook is organized into five parts:

Part 1 considers exact analytical results such as of product form type. Topics include characterization of product forms by physical balance concepts and simple traffic flow equations, classes of service and queue disciplines that allow a product form, a unified description of product forms for discrete time queueing networks, insights for insensitivity, and aggregation and decomposition results that allow sub networks to be aggregated into single nodes to reduce computational burden.

""

Part 2 looks at monotonicity and comparison results such as for computational simplification by either of two approaches: stochastic monotonicity and ordering results based on the ordering of the process generators, and comparison results and explicit error bounds based on an underlying Markov reward structure leading to ordering of expectations of performance measures.

""

Part 3 presents diffusion and fluid results. It specifically looks at the fluid regime and the diffusion regime. Both of these are illustrated through fluid limits for the analysis of system stability, diffusion approximations for multi-server systems, and a system fed by Gaussian traffic.

Part 4 illustrates computational and approximate results through the classical MVA (mean value analysis) and QNA (queueing network analyzer) for computing mean and variance of performance measures such as queue lengths and sojourn times; numerical approximation of response time distributions; and approximate decomposition results for large open queueing networks.

""

Part 5 enlightens selected applications as loss networks originating from circuit switched telecommunications applications, capacity sharing originating from packet switching in data networks, and a hospital application that is of growing present day interest.

The book shows that the intertwined progress of theory and practice will remain to be most intriguing and will continue to be the basis of further developments in queueing networks."

Applications of Supply Chain Management and E-Commerce Research (Hardcover, 2005 ed.): Joseph Geunes, Elif Akcali, Panos M.... Applications of Supply Chain Management and E-Commerce Research (Hardcover, 2005 ed.)
Joseph Geunes, Elif Akcali, Panos M. Pardalos, H.Edwin Romeijn, Zuo-Jun (Max) Shen
R3,158 Discovery Miles 31 580 Ships in 10 - 15 working days

In February 2002, the Industrial and Systems Engineering (ISE) De partment at the University of Florida hosted a National Science Founda tion Workshop on Collaboration and Negotiation in Supply Chain Man agement and E Commerce. This workshop focused on characterizing the challenges facing leading edge firms in supply chain management and electronic commerce, and identifying research opportunities for de veloping new technological and decision support capabilities sought by industry. The audience included practitioners in the areas of supply chain management and E Commerce, as well as academic researchers working in these areas. The workshop provided a unique setting that has facilitated ongoing dialog between academic researchers and industry practitioners. This book codifies many of the important themes and issues around which the workshop discussions centered. The editors of this book, all faculty members in the ISE Department at the University of Florida, also served as the workshop's coordinators. In addition to workshop participants, we also invited contributions from leading academics and practitioners who were not able to attend. As a result, the chapters herein represent a collection of research contributions, monographs, and case studies from a variety of disciplines and viewpoints. On the aca demic side alone, chapter authors include faculty members in supply chain and operations management, marketing, industrial engineering, economics, computer science, civil and environmental engineering, and building construction departments.

Linear and Nonlinear Programming - Second Edition (Hardcover, 2nd ed. 2003): David G. Luenberger Linear and Nonlinear Programming - Second Edition (Hardcover, 2nd ed. 2003)
David G. Luenberger
R3,665 Discovery Miles 36 650 Ships in 10 - 15 working days

The original edition of this book was celebrated for its coverage of the central concepts of practical optimization techniques. This updated edition expands and illuminates the connection between the purely analytical character of an optimization problem, expressed by properties of the necessary conditions, and the behavior of algorithms used to solve a problem. Incorporating modern theoretical insights, this classic text is even more useful.

Introduction to Nonlinear and Global Optimization (Hardcover, 2010 Ed.): Eligius M. T. Hendrix, Boglarka G. -Toth Introduction to Nonlinear and Global Optimization (Hardcover, 2010 Ed.)
Eligius M. T. Hendrix, Boglarka G. -Toth
R1,539 Discovery Miles 15 390 Ships in 10 - 15 working days

Nonlinear Optimization is an intriguing area of study where mathematical theory, algorithms and applications converge to calculate the optimal values of continuous functions. Within this subject, Global Optimization aims at finding global optima for difficult problems in which many local optima might exist.

This book provides a compelling introduction to global and non-linear optimization providing interdisciplinary readers with a strong background to continue their studies into these and other related fields. The book offers insight in relevant concepts such as "region of attraction" and "Branch-and-Bound" by elaborating small numerical examples and exercises for the reader to follow.

Multiobjective Linear and Integer Programming (Hardcover, 1st ed. 2016): Carlos Henggeler Antunes, Maria Joao Alves, Joao... Multiobjective Linear and Integer Programming (Hardcover, 1st ed. 2016)
Carlos Henggeler Antunes, Maria Joao Alves, Joao Climaco
R3,714 Discovery Miles 37 140 Ships in 12 - 17 working days

This book opens the door to multiobjective optimization for students in fields such as engineering, management, economics and applied mathematics. It offers a comprehensive introduction to multiobjective optimization, with a primary emphasis on multiobjective linear programming and multiobjective integer/mixed integer programming. A didactic book, it is mainly intended for undergraduate and graduate students, but can also be useful for researchers and practitioners. Further, it is accompanied by an interactive software package - developed by the authors for Windows platforms - which can be used for teaching and decision-making support purposes in multiobjective linear programming problems. Thus, besides the textbook's coverage of the essential concepts, theory and methods, complemented with illustrative examples and exercises, the computational tool enables students to experiment and enhance their technical skills, as well as to capture the essential characteristics of real-world problems.

Advanced Linear Modeling - Multivariate, Time Series, and Spatial Data; Nonparametric Regression and Response Surface... Advanced Linear Modeling - Multivariate, Time Series, and Spatial Data; Nonparametric Regression and Response Surface Maximization (Hardcover, 2nd ed. 2001)
Ronald Christensen
R2,334 R1,688 Discovery Miles 16 880 Save R646 (28%) Ships in 12 - 17 working days

This book introduces several topics related to linear model theory: multivariate linear models, discriminant analysis, principal components, factor analysis, time series in both the frequency and time domains, and spatial data analysis. The second edition adds new material on nonparametric regression, response surface maximization, and longitudinal models. The book provides a unified approach to these disparate subject and serves as a self-contained companion volume to the author's Plane Answers to Complex Questions: The Theory of Linear Models. Ronald Christensen is Professor of Statistics at the University of New Mexico. He is well known for his work on the theory and application of linear models having linear structure. He is the author of numerous technical articles and several books and he is a Fellow of the American Statistical Association and the Institute of Mathematical Statistics. Also Available: Christensen, Ronald. Plane Answers to Complex Questions: The Theory of Linear Models, Second Edition (1996). New York: Springer-Verlag New York, Inc. Christensen, Ronald. Log-Linear Models and Logistic Regression, Second Edition (1997). New York: Springer-Verlag New York, Inc.

Supply Chain Optimization (Hardcover, 2005 ed.): Joseph Geunes, Panos M. Pardalos Supply Chain Optimization (Hardcover, 2005 ed.)
Joseph Geunes, Panos M. Pardalos
R4,489 Discovery Miles 44 890 Ships in 12 - 17 working days

Supply Chain Optimization captures the latest results in a segment of current research activity in supply chain management. This research area focuses on applying optimization techniques to supply chain management problems. The research papers that make up the volume provide a snapshot of state-of-the-art optimization methods within the field. This book presents rigorous modelling approaches for supply chain operations problems with a goal of improving supply chain performance (or the performance of some segment thereof). It contains high-quality works from leading researchers in the field whose expertise fits within this scope. The book provides a diverse blend of research topics and novel modelling and solution approaches for difficult classes of supply chain operations, planning, and design problems.

Interior Point Methods for Linear Optimization (Hardcover, 2nd Revised edition): Cornelis Roos, Tamas Terlaky, J.-Ph. Vial Interior Point Methods for Linear Optimization (Hardcover, 2nd Revised edition)
Cornelis Roos, Tamas Terlaky, J.-Ph. Vial
R1,712 Discovery Miles 17 120 Ships in 12 - 17 working days

The era of interior point methods (IPMs) was initiated by N. Karmarkar's 1984 paper, which triggered turbulent research and reshaped almost all areas of optimization theory and computational practice. This book offers comprehensive coverage of IPMs. It details the main results of more than a decade of IPM research. Numerous exercises are provided to aid in understanding the material.

In-Depth Analysis of Linear Programming (Hardcover, 2001 ed.): F.P. Vasilyev, A.Y. Ivanitskiy In-Depth Analysis of Linear Programming (Hardcover, 2001 ed.)
F.P. Vasilyev, A.Y. Ivanitskiy
R3,059 Discovery Miles 30 590 Ships in 10 - 15 working days

Along with the traditional material concerning linear programming (the simplex method, the theory of duality, the dual simplex method), In-Depth Analysis of Linear Programming contains new results of research carried out by the authors. For the first time, the criteria of stability (in the geometrical and algebraic forms) of the general linear programming problem are formulated and proved. New regularization methods based on the idea of extension of an admissible set are proposed for solving unstable (ill-posed) linear programming problems. In contrast to the well-known regularization methods, in the methods proposed in this book the initial unstable problem is replaced by a new stable auxiliary problem. This is also a linear programming problem, which can be solved by standard finite methods. In addition, the authors indicate the conditions imposed on the parameters of the auxiliary problem which guarantee its stability, and this circumstance advantageously distinguishes the regularization methods proposed in this book from the existing methods. In these existing methods, the stability of the auxiliary problem is usually only presupposed but is not explicitly investigated. In this book, the traditional material contained in the first three chapters is expounded in much simpler terms than in the majority of books on linear programming, which makes it accessible to beginners as well as those more familiar with the area.

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