Springer Optimization and Its Applications

Panos M. Pardalos · Themistocles M. Rassias · Alexander J. Zaslavski · Nicholas J. Daras

Latest release: January 4, 2024

Series

198

Books

Optimization Theory and Methods: Nonlinear Programming

Book 1·Aug 2006

Optimization Theory and Methods can be used as a textbook for an optimization course for graduates and senior undergraduates. It is the result of the author's teaching and research over the past decade. It describes optimization theory and several powerful methods. For most methods, the book discusses an idea’s motivation, studies the derivation, establishes the global and local convergence, describes algorithmic steps, and discusses the numerical performance.

Optimization with Multivalued Mappings: Theory, Applications and Algorithms

Book 2·Sep 2006

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In the field of nondifferentiable nonconvex optimization, one of the most intensely investigated areas is that of optimization problems involving multivalued mappings in constraints or as the objective function. This book focuses on the tremendous development in the field that has taken place since the publication of the most recent volumes on the subject. The new topics studied include the formulation of optimality conditions using different kinds of generalized derivatives for set-valued mappings (such as, for example, the coderivative of Mordukhovich), the opening of new applications (e.g., the calibration of water supply systems), or the elaboration of new solution algorithms (e.g., smoothing methods).

The book is divided into three parts. The focus in the first part is on bilevel programming. The chapters in the second part contain investigations of mathematical programs with equilibrium constraints. The third part is on multivalued set-valued optimization. The chapters were written by outstanding experts in the areas of bilevel programming, mathematical programs with equilibrium (or complementarity) constraints (MPEC), and set-valued optimization problems.

Optimization in Public Transportation: Stop Location, Delay Management and Tariff Zone Design in a Public Transportation Network

Book 3·Jan 2007

5.0

Customer-Oriented Optimization in Public Transportation develops models, results and algorithms for optimizing public transportation from a customer-oriented point of view. The methods used are based on graph-theoretic approaches and integer programming. The specific topics are all motivated by real-world examples which occurred in practical projects. An appendix summarizes some of the basics of optimization needed to interpret the material in the book.

In detail, the topics the book covers in its three parts are as follows:

1. Stop location. Does it make sense to open new stations along existing bus or railway lines? If yes, in which locations? The problem is modeled as a continuous covering problem. To solve it the author develops a finite dominating set and shows that efficient methods are possible if the special structure of the covering matrix is used.

2. Delay management. Should a train wait for delayed feeder trains or should it depart in time? The author builds up two different integer programming models and a model based on project planning methods. Properties and solution methods are developed.

3. Tariff planning. Part 3 deals with the design of zone tariff systems, in which the fare is determined by the number of zones used by the passengers. The author presents a model for this problem and approaches based on clustering theory.

Models and Algorithms for Global Optimization: Essays Dedicated to Antanas Žilinskas on the Occasion of His 60th Birthday

Book 4·Apr 2007

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Antanas ~ilinskas was born on January 5, 1946 in Lithuania. He graduated with a gold medal from 2nd Kaunas Gymnasium in 1963 and with a distinction diploma of Electrical Engineering from Kaunas University of Technology in 1968. His Ph. D. studies (aspirantur) at Lithuanian Academy of Sciences lasted from 1970 to 1973. The Candidate of Sciences (Ph. D. ) degree in Technical - bernetics (1973) has been received from Kaunas University of Technology. The Doctor of Mathematical Sciences degree (Habilitation, 1985) has been received from St. Petersburg (Leningrad) University. The title Senior Research Fellow (1980) has been conferred by the Presidium of Academy of Sciences, and the title Professor (1989) by Vilnius Pedagogical University. He has been awarded (with V. saltenis and G. Dzemyda) Lithuanian National Award for scientific achievements of 2001 for the research on "Efficient optimization methods and their applications". A. ~ilinskas joined the Institute of Mathematics and Informatics in 1973 starting with a position of junior research associate, worked as a senior - search associate reaching the highest rank of principal researcher which is his main position now. Apart from working in the research institute he was a lecturer at Vilnius Pedagogical University 1986-1988, where he founded a - partment of Informatics in 1988 and held a position of professor and head of this department 1988-1993. He worked later as a professor of this department until 2000.

Differential Evolution: In Search of Solutions

Book 5·Feb 2007

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Di?erential evolution is one of the most recent global optimizers. Discovered in 1995 it rapidly proved its practical e?ciency. This book gives you a chance to learn all about di?erential evolution. On reading it you will be able to pro?tably apply this reliable method to problems in your ?eld. Asforme,mypassionforintelligentsystemsandoptimizationbeganasfar back as during my studies at Moscow State Technical University of Bauman, the best engineering school in Russia. At that time, I was gathering material for my future thesis. Being interested in my work, the Mining School of Paris proposed that I write a dissertation in France. I hesitated some time over a choice, but my natural curiosity and taste for novelty ?nally prevailed. At ́ present, Docteur ` es science en informatique de l’EcoledesMinesdeParis,I am concentrating on the development of my own enterprise. If optimization is my vocation, my hobbies are mathematics and music. Although mathematics disciplines the mind, music is ?lled with emotions. While playing my favorite composition, I decided to write this book. The purpose of the book is to give, in a condensed but overview form, a description of di?erential evolution. In addition, this book makes accessible to a wide audience the fruits of my long research in optimization. Namely, I laid the foundation of the universal concept of search strategies design, suitable not only for di?erential evolution but for many other algorithms. Also, I introduced a principle of energetic selection, an e?cient method of hybridization, and advanced paralleling techniques.

New Approaches to Circle Packing in a Square: With Program Codes

Book 6·May 2007

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In one sense, the problem of finding the densest packing of congruent circles in a square is easy to understand. But on closer inspection, this problem reveals itself to be an interesting challenge of discrete and computational geometry with all its surprising structural forms and regularities. This book summarizes results achieved in solving the circle packing problem over the past few years, providing the reader with a comprehensive view of both theoretical and computational achievements. Typically illustrations of problem solutions are shown, elegantly displaying the results obtained.

Beyond the theoretically challenging character of the problem, the solution methods developed in the book also have many practical applications.

Since the codes can be worked with directly, they will enable the reader to improve on them and solve problem instances that still remain challenging, or to use them as a starting point for solving related application problems.

Data Mining in Biomedicine

Book 7·Dec 2008

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This volume presents an extensive collection of contributions covering aspects of the exciting and important research field of data mining techniques in biomedicine. Coverage includes new approaches for the analysis of biomedical data; applications of data mining techniques to real-life problems in medical practice; comprehensive reviews of recent trends in the field. The book addresses incorporation of data mining in fundamental areas of biomedical research: genomics, proteomics, protein characterization, and neuroscience.

Set-Valued Mappings and Enlargements of Monotone Operators

Book 8·Nov 2007

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Set-valued analysis is an essential tool for the mathematical formulation of many real-life situations, e.g., equilibrium theory in mathematical economics. This work offers the first comprehensive treatment in book form of the fairly new subdiscipline of enlargements of maximal monotone operators, including several important new results in the field. In the last decades, with the development of nonsmooth optimization, effective algorithms have been developed to solve these kinds of problems, such as nonsmooth variational inequalities. Several of these methods, such as bundle methods for variational problems, are fully developed and analyzed in this book.

The first chapters provide a self-contained review of the basic notions and fundamental results in set-valued analysis, including set convergence and continuity of set-valued mappings together with many important results in infinite-dimensional convex analysis, leading to the classical fixed point results due to Ekeland, Caristi and Kakutani. Next, an in-depth introduction to monotone operators is developed, emphasizing results related to maximality of subdifferentials and of sums of monotone operators. Building on this foundational material, the second part of the monograph contains new results (all of them established during the last decade) on the concept of enlargements of monotone operators, with applications to variational inequalities, bundle-type methods, augmented Lagrangian methods, and proximal point algorithms.

Audience:
This book is addressed to mathematicians, engineers, economists, and researchers interested in acquiring a solid mathematical foundation in topics such as point-to-set operators, variational inequalities, general equilibrium theory, and nonsmooth optimization, among others. Containing extensive exercises and examples throughout the text, the first four chapters of the book can also be used for a one-quarter course in set-valued analysis and maximal monotone operators for graduate students in pure and applied mathematics, mathematical economics, operations research and related areas. The only requisites, besides a minimum level of mathematical maturity, are some basic results of general topology and functional analysis.

Stochastic Global Optimization

Book 9·Nov 2007

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This book aims to cover major methodological and theoretical developments in the ?eld of stochastic global optimization. This ?eld includes global random search and methods based on probabilistic assumptions about the objective function. We discuss the basic ideas lying behind the main algorithmic schemes, formulate the most essential algorithms and outline the ways of their theor- ical investigation. We try to be mathematically precise and sound but at the same time we do not often delve deep into the mathematical detail, referring instead to the corresponding literature. We often do not consider the most g- eral assumptions, preferring instead simplicity of arguments. For example, we only consider continuous ?nite dimensional optimization despite the fact that some of the methods can easily be modi?ed for discrete or in?nite-dimensional optimization problems. The authors’ interests and the availability of good surveys on particular topics have in uenced the choice of material in the book. For example, there are excellent surveys on simulated annealing (both on theoretical and - plementation aspects of this method) and evolutionary algorithms (including genetic algorithms). We thus devote much less attention to these topics than they merit, concentrating instead on the issues which are not that well d- umented in literature. We also spend more time discussing the most recent ideas which have been proposed in the last few years.

Nonsmooth Vector Functions and Continuous Optimization

Book 10·Oct 2007

2.0

A recent significant innovation in mathematical sciences has been the progressive use of nonsmooth calculus, an extension of the differential calculus, as a key tool of modern analysis in many areas of mathematics, operations research, and engineering. Focusing on the study of nonsmooth vector functions, this book presents a comprehensive account of the calculus of generalized Jacobian matrices and their applications to continuous nonsmooth optimization problems and variational inequalities in finite dimensions.

The treatment is motivated by a desire to expose an elementary approach to nonsmooth calculus by using a set of matrices to replace the nonexistent Jacobian matrix of a continuous vector function. Such a set of matrices forms a new generalized Jacobian, called pseudo-Jacobian. A direct extension of the classical derivative that follows simple rules of calculus, the pseudo-Jacobian provides an axiomatic approach to nonsmooth calculus, a flexible tool for handling nonsmooth continuous optimization problems.

Illustrated by numerous examples of known generalized derivatives, the work may serve as a valuable reference for graduate students, researchers, and applied mathematicians who wish to use nonsmooth techniques and continuous optimization to model and solve problems in mathematical programming, operations research, and engineering. Readers require only a modest background in undergraduate mathematical analysis to follow the material with minimal effort.

Optimization and Control of Bilinear Systems: Theory, Algorithms, and Applications

Book 11·Mar 2010

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The present book is based on results of scienti?c investigations and on the materials of special courses, o?ered for graduate and undergraduate students. The purpose of this book is to acquaint the reader with the developments in bilinear systems theory and its applications. Particular attention is paid to control of open physical processes functioning in a nonequilibrium mode. The text consists of eight chapters. Chapter 1 is concerned with the problems of systems analysis of bilinear processes. Chapter 2 solves the problem of optimal control of bilinear systems on the basis of di?er- tial geometry methods. Chapter 3 deals with the progress made in an adaptive estimation technique. Chapter 4 is devoted to the application of the Yang–Mills ?elds to investigation of nonlinear control problems. Chapter 5 considers intelligent sensors, used to examine weak signals. This chapter also describes and analyzes bilinear models of intelligent sensing elements. Chapter 6 illustrates control problems of a quantum system. Chapter 7 discusses the problems of control and identi?cation in systems with chaotic dynamics. Finally, Chapter 8 examines the c- trolled processes running in biomolecular systems. This book is directed to students, postgraduate students, and speci- ists engaged in the ?elds of control of physical processes, quantum and molecular computing, biophysics, and physical information science.

Optimization in Medicine

Book 12·Dec 2007

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Optimization has become an essential tool in addressing the limitation of resources and need for better decision-making in the medical field. Both continuous and discrete mathematical techniques are playing an increasingly important role in understanding several fundamental problems in medicine.

This volume presents a wide range of medical applications that can utilize mathematical computing. Examples include using an algorithm for considering the seed reconstruction problem in brachytherapy and using optimization-classification models to assist in the early prediction, diagnosis and detection of diseases. Discrete optimization techniques and measures derived from the theory of nonlinear dynamics, with analysis of multi-electrode electroencephalographic (EEG) data, assist in predicting impending epileptic seizures. Mathematics in medicine can also be found in recent cancer research. Sophisticated mathematical models and optimization algorithms have been used to generate treatment plans for radionuclide implant and external beam radiation therapy. Optimization techniques have also been used to automate the planning process in Gamma Knife treatment, as well as to address a variety of medical image registration problems.

This work grew out of a workshop on optimization which was held during the 2005 CIM Thematic Term on Optimization in Coimbra, Portugal. It provides an overview of the state-of-the-art in optimization in medicine and will serve as an excellent reference for researchers in the medical computing community and for those working in applied mathematics and optimization.

Scalar and Asymptotic Scalar Derivatives: Theory and Applications

Book 13·May 2008

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This book is devoted to the study of scalar and asymptotic scalar derivatives and their applications to the study of some problems considered in nonlinear analysis, in geometry, and in applied mathematics. The notion of a scalar derivative is due to S. Z. Nemeth, ́ and the notion of an asymptotic scalar derivative is due to G. Isac. Both notions are recent, never considered in a book, and have interesting applications. About applications, we cite applications to the study of complementarity problems, to the study of xed points of nonlinear mappings, to spectral nonlinear analysis, and to the study of some interesting problems considered in differential geometry and other applications. A new characterization of monotonicity of nonlinear mappings is another remarkable application of scalar derivatives. A relation between scalar derivatives and asymptotic scalar derivatives, - alized by an inversion operator is also presented in this book. This relation has important consequences in the theory of scalar derivatives, and in some applications. For example, this relation permitted us a new development of the method of exceptional family of elements, introduced and used by G. Isac in complementarity theory. Now, we present a brief description of the contents of this book. Chapter 1 is dedicated to the study of scalar derivatives in Euclidean spaces.

V-Invex Functions and Vector Optimization

Book 14·Nov 2007

4.0

This volume summarizes and synthesizes an aspect of research work that has been done in the area of Generalized Convexity over the past few decades. Specifically, the book focuses on V-invex functions in vector optimization that have grown out of the work of Jeyakumar and Mond in the 1990’s. The authors integrate related research into the book and demonstrate the wide context from which the area has grown and continues to grow.

Country Risk Evaluation: Methods and Applications

Book 15·Jul 2010

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Financial globalization has increased the significance of methods used in the evaluation of country risk, one of the major research topics in economics and finance. Written by experts in the fields of multicriteria methodology, credit risk assessment, operations research, and financial management, this book develops a comprehensive framework for evaluating models based on several classification techniques that emerge from different theoretical directions. This book compares different statistical and data mining techniques, noting the advantages of each method, and introduces new multicriteria methodologies that are important to country risk modeling.

Key topics include: (1) A review of country risk definitions and an overview of the most recent tools in country risk management, (2) In-depth analysis of statistical, econometric and non-parametric classification techniques, (3) Several real-world applications of the methodologies described throughout the text, (4) Future research directions for country risk assessment problems.

This work is a useful toolkit for economists, financial managers, bank managers, operations researchers, management scientists, and risk analysts. Moreover, the book can also be used as a supplementary text for graduate courses in finance and financial risk management.

Fuzzy Multi-Criteria Decision Making: Theory and Applications with Recent Developments

Book 16·Aug 2008

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In trying to make a satisfactory decision when imprecise and multicriteria situations are involved, a decision maker has to use a fuzzy multicriteria decision making method. "Fuzzy Multi-Criteria Decision Making" (MCDM) presents fuzzy multiattribute and multiobjective decision-making methodologies by distinguished MCDM researchers.

In summarizing the concepts and results of the most popular fuzzy multicriteria methods, using numerical examples, this work examines all the fuzzy multicriteria methods recently developed, such as fuzzy AHP, fuzzy TOPSIS, interactive fuzzy multiobjective stochastic linear programming, fuzzy multiobjective dynamic programming, grey fuzzy multiobjective optimization, fuzzy multiobjective geometric programming, and more. Each of the 22 chapters includes practical applications along with new developments/results.

This book may be used as a textbook in graduate operations research, industrial engineering, and economics courses. It will also be an excellent resource, providing new suggestions and directions for further research, for computer programmers, mathematicians, and scientists in a variety of disciplines where multicriteria decision making is needed.

Handbook of Financial Engineering

Book 18·Jul 2010

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Over the past decade the financial and business environments have undergone significant changes. During the same period several advances have been made within the field of financial engineering, involving both the methodological tools as well as the application areas.

This comprehensive edited volume discusses the most recent advances within the field of financial engineering, focusing not only on the description of the existing areas in financial engineering research, but also on the new methodologies that have been developed for modeling and addressing financial engineering problems.

This book is divided into four major parts, each covering different aspects of financial engineering and modeling such as portfolio management and trading, risk management, applications of operation research methods, and credit rating models.

Handbook of Financial Engineering is intended for financial engineers, researchers, applied mathematicians, and graduate students interested in real-world applications to financial engineering.