We always come cross several decision-making problems in our daily life. Such problems are always conflicting in which many different view points should be satisfied. In politics, business, industrial systems, management science, networks, etc. one often encounters such kind of problems. The most important and difficult part in such problems is the conflict between various objectives and goals. In these problems, one has to find the minimum(or maximum) for several objective functions. Such problems are called vector optimization problems (VOP),multi-criteria optimization problems or multi-objective optimization problems. This volume deals with several different topics / aspects of vector optimization theory ranging from the very beginning to the most recent one. It contains fourteen chapters written by different experts in the field of vector optimization.

The study of the theory of games was started in Von Neumann (1928), but the development of the theory of games was accelerated after the publication of the classical book "Theory of games and economic behavior" by Von Neumann and Morgenstern (1944). As an initial step, the theory of games aims to put situations of conflict and cooperation into mathematical models. In the second and final step, the resulting models are analysed on the basis of equitable and mathematical reasonings. The conflict and/or cooperative situation in question is generally due to the interaction between two or more individuals (players). Their interaction may lead up to several potential payoffs over which each player has his own preferences. Any player attempts to achieve his largest possible payoff, but the other players may also exert their influence on the realization of some potential payoff. As already mentioned, the theory of games consists of two parts, a modelling part and a solution part. Concerning the modelling part, the mathematical models of conflict and cooperative situations are described. The description of the models includes the rules, the strategy space of any player, potential payoffs to the players, the preferences of each player over the set of all potential payoffs, etc. According to the rules, it is either permitted or forbidden that the players communicate with one another in order to make binding agreements regarding their mutual actions.

Give, and it shall be given unto you. ST. LUKE, VI, 38. The book is based on several courses of lectures on control theory and appli cations which were delivered by the authors for a number of years at Moscow Electronics and Mathematics University. The book, originally written in Rus sian, was first published by Vysshaya Shkola (Higher School) Publishing House in Moscow in 1989. In preparing a new edition of the book we planned to make only minor changes in the text. However, we soon realized that we like many scholars working in control theory had learned many new things and had had many new insights into control theory and its applications since the book was first published. Therefore, we rewrote the book especially for the English edition. So, this is substantially a new book with many new topics. The book consists of an introduction and four parts. Part One deals with the fundamentals of modern stability theory: general results concerning stability and instability, sufficient conditions for the stability of linear systems, methods for determining the stability or instability of systems of various type, theorems on stability under random disturbances."

Many books on optimization consider only finite dimensional spaces. This volume is unique in its emphasis: the first three chapters develop optimization in spaces without linear structure, and the analog of convex analysis is constructed for this case. Many new results have been proved specially for this publication. In the following chapters optimization in infinite topological and normed vector spaces is considered. The novelty consists in using the drop property for weak well-posedness of linear problems in Banach spaces and in a unified approach (by means of the Dolecki approximation) to necessary conditions of optimality. The method of reduction of constraints for sufficient conditions of optimality is presented. The book contains an introduction to non-differentiable and vector optimization. Audience: This volume will be of interest to mathematicians, engineers, and economists working in mathematical optimization.

This is an open access book discusses readers to various methods of modeling plans and policies that address public sector issues and problems. Written for public policy and social sciences students at the upper undergraduate and graduate level, as well as public sector decision-makers, it demonstrates and compares the development and use of various deterministic and probabilistic optimization and simulation modeling methods for analyzing planning and management issues. These modeling tools offer a means of identifying and evaluating alternative plans and policies based on their physical, economic, environmental, and social impacts. Learning how to develop and use the mathematical modeling tools introduced in this book will give students useful skills when in positions of having to make informed public policy recommendations or decisions.

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, as well as variational inequalities in finite dimensions. The treatment is motivated by a desire to expose an elementary approach to nonsmooth calculus, using a set of matrices to replace the nonexistent Jacobian matrix of a continuous vector function.

This monograph presents a comprehensive treatment of the maximum-entropy sampling problem (MESP), which is a fascinating topic at the intersection of mathematical optimization and data science. The text situates MESP in information theory, as the algorithmic problem of calculating a sub-vector of pre-specificed size from a multivariate Gaussian random vector, so as to maximize Shannon's differential entropy. The text collects and expands on state-of-the-art algorithms for MESP, and addresses its application in the field of environmental monitoring. While MESP is a central optimization problem in the theory of statistical designs (particularly in the area of spatial monitoring), this book largely focuses on the unique challenges of its algorithmic side. From the perspective of mathematical-optimization methodology, MESP is rather unique (a 0/1 nonlinear program having a nonseparable objective function), and the algorithmic techniques employed are highly non-standard. In particular, successful techniques come from several disparate areas within the field of mathematical optimization; for example: convex optimization and duality, semidefinite programming, Lagrangian relaxation, dynamic programming, approximation algorithms, 0/1 optimization (e.g., branch-and-bound), extended formulation, and many aspects of matrix theory. The book is mainly aimed at graduate students and researchers in mathematical optimization and data analytics.

Many of the most challenging problems in the applied sciences involve non-differentiable structures as well as partial differential operators, thus leading to non-smooth distributed parameter systems. This edited volume aims to establish a theoretical and numerical foundation and develop new algorithmic paradigms for the treatment of non-smooth phenomena and associated parameter influences. Other goals include the realization and further advancement of these concepts in the context of robust and hierarchical optimization, partial differential games, and nonlinear partial differential complementarity problems, as well as their validation in the context of complex applications. Areas for which applications are considered include optimal control of multiphase fluids and of superconductors, image processing, thermoforming, and the formation of rivers and networks. Chapters are written by leading researchers and present results obtained in the first funding phase of the DFG Special Priority Program on Nonsmooth and Complementarity Based Distributed Parameter Systems: Simulation and Hierarchical Optimization that ran from 2016 to 2019.

This book collects chapters on contemporary topics on metric fixed point theory and its applications in science, engineering, fractals, and behavioral sciences. Chapters contributed by renowned researchers from across the world, this book includes several useful tools and techniques for the development of skills and expertise in the area. The book presents the study of common fixed points in a generalized metric space and fixed point results with applications in various modular metric spaces. New insight into parametric metric spaces as well as study of variational inequalities and variational control problems have been included.

The field of metaheuristics has been fast evolving in recent years. Techniques such as simulated annealing, tabu search, genetic algorithms, scatter search, greedy randomized adaptive search, variable neighborhood search, ant systems, and their hybrids are currently among the most efficient and robust optimization strategies to find high-quality solutions to many real-life optimization problems. A very large number of successful applications of metaheuristics are reported in the literature and spread throughout many books, journals, and conference proceedings. A series of international conferences entirely devoted to the theory, applications, and computational developments in metaheuristics has been attracting an increasing number of participants, from universities and the industry. Essays and Surveys in Metaheuristics goes beyond the recent conference-oriented volumes in Metaheuristics, with its focus on surveys of recent developments of the main metaheuristics. Well-known specialists have written surveys on the following subjects: simulated annealing (E. Aarts and J. Korst, The Netherlands), noising methods (I. Charon and O. Hudry, France), strategies for the parallel implementation of metaheuristics (V.-D. Cung and C. Roucairol, France, and S.L. Martins and C.C. Ribeiro, Brazil), greedy randomized adaptive search procedures (P. Festa, Italy, and M.G.C. Resende, USA), tabu search (M. Gendreau, Canada), variable neighborhood search (P. Hansen and N. Mladenovic, Canada), ant colonies (V. Maniezzo and A. Carbonaro, Italy), and evolutionary algorithms (H. MA1/4hlenbein and Th. Mahnig, Germany). Several further essays address issues or variants of metaheuristics, as well as innovative orsuccessful applications of metaheuristics to classical or new combinatorial optimization problems.

Games, Norms, and Reasons: Logic at the Crossroads provides an overview of modern logic focusing on its relationships with other disciplines, including new interfaces with rational choice theory, epistemology, game theory and informatics. This book continues a series called "Logic at the Crossroads" whose title reflects a view that the deep insights from the classical phase of mathematical logic can form a harmonious mixture with a new, more ambitious research agenda of understanding and enhancing human reasoning and intelligent interaction. The editors have gathered together articles from active authors in this new area that explore dynamic logical aspects of norms, reasons, preferences and beliefs in human agency, human interaction and groups. The book pays a special tribute to Professor Rohit Parikh, a pioneer in this movement.

This book presents and uses a major, new database of the most serious forms of internal resistance to the Nazi state to study empirically the whole phenomenon of resistance to an authoritarian regime. By studying serious political resistance from a quantitative historical perspective, the book opens up a new avenue of research for economic history. The database underpinning the book was painstakingly compiled from official state records of treason and/or high treason tried before the German People's Court (Volksgerichtshof) between 1933 and 1945. It brings together material on resistance groups stored in the archives of the Federal Republic of Germany and Austria with previously inaccessible files from the former German Democratic Republic, Czechoslovakia and Soviet Union. Through searching these records, the authors have been able to reconstruct in hitherto unattainable detail the economic, social, political, ethnic and familial profiles, backgroun ds, and influences of all 4,378 civilians of the Third Reich active in Germany, Austria and the outside territories for whom there are complete records. The findings of their research afford fresh, new interdisciplinary insights and perspectives, not only on the configuration, timing, impact and profile of resistance to the Nazi state, but also on a range of real-world behaviours common within authoritarian states, such as defection, reward and punishment, and commitment to group identities. The book's statistical analysis reveals precisely the who, how, where and when of serious resistance. In so doing, it advances significantly our understanding of the overall pattern and nature of serious resistance within Nazi Germany.

Operations Research in Space and Air is a selection of papers reflecting the experience and expertise of international OR consulting companies and academic groups. The global market and competition play a crucial part in the decision making processes within the Space and Air industries and this book gives practical examples of how advanced applications can be used by Space and Air industry management. The material within the book provides both the basic background for the novice modeler and a useful reference for experienced modelers. Students, researchers and OR practitioners will appreciate the details of the modeling techniques, the processes that have been implemented and the computational results that demonstrate the benefits in applying OR in the Space and Airline industries. Advances in PC and Workstations technology, in optimiza tion engines and in modeling techniques now enable solving problems, never before attained by Operations Research. In recent years the Ital ian OR Society (AfRO, www. airo. org) has organized annual forums for researchers and practitioners to meet together to present and dis cuss the various scientific and technical OR achievements. The OR in Space 8 Air session of AfR02001 and AfR02002 Conferences, together with optimization tools' applications, presented recent results achieved by Alenia Spazio S. p. A. (Turin), Alitalia, Milan Polytechnic and Turin Polytechinc. With additional contributions from academia and indus try they have enabled us to capture, in print, today's 'state-of-the-art' optimization and data mining solutions."

The rich, multi-faceted and multi-disciplinary field of matching-based market design is an active and important one due to its highly successful applications with economic and sociological impact. Its home is economics, but with intimate connections to algorithm design and operations research. With chapters contributed by over fifty top researchers from all three disciplines, this volume is unique in its breadth and depth, while still being a cohesive and unified picture of the field, suitable for the uninitiated as well as the expert. It explains the dominant ideas from computer science and economics underlying the most important results on market design and introduces the main algorithmic questions and combinatorial structures. Methodologies and applications from both the pre-Internet and post-Internet eras are covered in detail. Key chapters discuss the basic notions of efficiency, fairness and incentives, and the way market design seeks solutions guided by normative criteria borrowed from social choice theory.

This book describes applications of Jaya and Rao algorithms on real case studies concerning different renewable energy sources. In the last few decades, researchers have focused on renewable energy resources like solar energy, bio-energy, wave energy, ocean thermal energy, tidal energy, geothermal energy, and wind energy. This has resulted in the development of new techniques and tools that could harvest energy from renewable energy sources. Many researchers and scientists have focused on developing and optimizing the energy systems to extract and utilize renewable energy more efficiently. In this book, recently developed Jaya and Rao (Rao-1, Rao-2, and Rao-3) algorithms are introduced for single- and multi-objective optimization of selected renewable energy systems. The results of applications of the different versions of Jaya and Rao algorithms are compared with the other optimization techniques like GA, NSGA-II, PSO, MOPSO, ABC, etc., and the performance of the Jaya and Rao algorithms is highlighted compared to other optimization algorithms in the case of renewable energy systems. The book also includes the validation of different versions of the Jaya and Rao algorithms through the application to complex single- and multi-objective unconstrained benchmark functions. The algorithms and computer codes of different version of Jaya and Rao algorithms are included in the book that will be very much useful to readers in industry and academic research.

This original and timely monograph describes a unique self-contained excursion that reveals to the readers the roles of two basic cognitive abilities, i.e. intention recognition and arranging commitments, in the evolution of cooperative behavior. This book analyses intention recognition, an important ability that helps agents predict others behavior, in its artificial intelligence and evolutionary computational modeling aspects, and proposes a novel intention recognition method. Furthermore, the book presents a new framework for intention-based decision making and illustrates several ways in which an ability to recognize intentions of others can enhance a decision making process. By employing the new intention recognition method and the tools of evolutionary game theory, this book introduces computational models demonstrating that intention recognition promotes the emergence of cooperation within populations of self-regarding agents. Finally, the book describes how commitment provides a pathway to the evolution of cooperative behavior, and how it further empowers intention recognition, thereby leading to a combined improved strategy. "

This monograph covers one of the divisions of mathematical theory of control which examines moving objects functionating under conflict and uncertainty conditions. To identify this range of problems we use the term "conflict con trolled processes," coined in recent years. As the name itself does not imply the type of dynamics (difference, ordinary differential, difference-differential, integral, or partial differential equations) the differential games falI within its realms. The problems of search and tracking moving objects are also referred to the field of conflict controlled process. The contents of the monograph is confined to studying classical pursuit-evasion problems which are central to the theory of conflict controlled processes. These problems underlie the theory and are of considerable interest to researchers up to now. It should be noted that the methods of "Line of Sight," "Parallel Pursuit," "Proportional N avigation,""Modified Pursuit" and others have been long and well known among engineers engaged in design of rocket and space technology. An abstract theory of dynamic game problems, in its turn, is based on the methods originated by R. Isaacs, L. S. Pontryagin, and N. N. Krasovskii, and on the approaches developed around these methods. At the heart of the book is the Method of Resolving Functions which was realized within the class of quasistrategies for pursuers and then applied to the solution of the problems of "hand-to-hand," group, and succesive pursuit."

In Linear Programming: A Modern Integrated Analysis, both boundary (simplex) and interior point methods are derived from the complementary slackness theorem and, unlike most books, the duality theorem is derived from Farkas's Lemma, which is proved as a convex separation theorem. The tedium of the simplex method is thus avoided. A new and inductive proof of Kantorovich's Theorem is offered, related to the convergence of Newton's method. Of the boundary methods, the book presents the (revised) primal and the dual simplex methods. An extensive discussion is given of the primal, dual and primal-dual affine scaling methods. In addition, the proof of the convergence under degeneracy, a bounded variable variant, and a super-linearly convergent variant of the primal affine scaling method are covered in one chapter. Polynomial barrier or path-following homotopy methods, and the projective transformation method are also covered in the interior point chapter. Besides the popular sparse Cholesky factorization and the conjugate gradient method, new methods are presented in a separate chapter on implementation. These methods use LQ factorization and iterative techniques.

This volume results from the "Second International Conference on Dynamics of Disasters" held in Kalamata, Greece, June 29-July 2, 2015. The conference covered particular topics involved in natural and man-made disasters such as war, chemical spills, and wildfires. Papers in this volume examine the finer points of disasters through: Critical infrastructure protection Resiliency Humanitarian logistic Relief supply chains Cooperative game theory Dynamical systems Decision making under risk and uncertainty Spread of diseases Contagion Funding for disaster relief Tools for emergency preparedness Response, and risk mitigation Multi-disciplinary theories, tools, techniques and methodologies are linked with disasters from mitigation and preparedness to response and recovery. The interdisciplinary approach to problems in economics, optimization, government, management, business, humanities, engineering, medicine, mathematics, computer science, behavioral studies, emergency services, and environmental studies will engage readers from a wide variety of fields and backgrounds.

The concept of "reformulation" has long been playing an important role in mathematical programming. A classical example is the penalization technique in constrained optimization that transforms the constraints into the objective function via a penalty function thereby reformulating a constrained problem as an equivalent or approximately equivalent unconstrained problem. More recent trends consist of the reformulation of various mathematical programming prob lems, including variational inequalities and complementarity problems, into equivalent systems of possibly nonsmooth, piecewise smooth or semismooth nonlinear equations, or equivalent unconstrained optimization problems that are usually differentiable, but in general not twice differentiable. Because of the recent advent of various tools in nonsmooth analysis, the reformulation approach has become increasingly profound and diversified. In view of growing interests in this active field, we planned to organize a cluster of sessions entitled "Reformulation - Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods" in the 16th International Symposium on Mathematical Programming (ismp97) held at Lausanne EPFL, Switzerland on August 24-29, 1997. Responding to our invitation, thirty-eight people agreed to give a talk within the cluster, which enabled us to organize thirteen sessions in total. We think that it was one of the largest and most exciting clusters in the symposium. Thanks to the earnest support by the speakers and the chairpersons, the sessions attracted much attention of the participants and were filled with great enthusiasm of the audience."

Optimization is a field important in its own right but is also integral to numerous applied sciences, including operations research, management science, economics, finance and all branches of mathematics-oriented engineering. Constrained optimization models are one of the most widely used mathematical models in operations research and management science.

This book gives a modern and well-balanced presentation of the subject, focusing on theory but also including algorithims and examples from various real-world applications. The text is easy to read and accessible to anyone with a knowledge of multi-dimensional calculus, linear algebra and basic numerical methods. Detailed examples and counter-examples are provided--as are exercises, solutions and helpful hints, and Matlab/Maple supplements.

The intended readership is advanced undergraduates, graduates, and professionals in any of the applied fields.

This work presents lines of investigation and scientific achievements of the Ukrainian school of optimization theory and adjacent disciplines. These include the development of approaches to mathematical theories, methodologies, methods, and application systems for the solution of applied problems in economy, finances, energy saving, agriculture, biology, genetics, environmental protection, hardware and software engineering, information protection, decision making, pattern recognition, self-adapting control of complicated objects, personnel training, etc. The methods developed include sequential analysis of variants, nondifferential optimization, stochastic optimization, discrete optimization, mathematical modeling, econometric modeling, solution of extremum problems on graphs, construction of discrete images and combinatorial recognition, etc. Some of these methods became well known in the world's mathematical community and are now known as classic methods.

Recent books in the Wiley Series in Probability and Mathematical Statistics Editors Vic Barnett J. Stuart Hunter Adrian F.M. Smith Geoffrey S. Watson Ralph A. Bradley Joseph B. Kadane Stephen M. Stigler Nicholas I. Fisher David G. Kendall Jozef L. Teugels Optimal Design of Experiments Friedrich Pukelsheim, Universität Augsburg, Augsburg, Germany Optimal Design of Experiments presents the first complete theoretical development of optimal design for the linear model, a unified exposition that embraces a wide variety of design problems. It describes the statistical theory involved in designing experiments, and applies it to typical special cases. The design problems originating from statistics are solved using tools from linear algebra and convex analysis. The material is presented in a very clear, careful and organized way. Rather than assaulting traditional ways of thinking about optimal design, this book pulls together formerly separate entities to create a common framework for diverse design problems that share a common goal. Statisticians, mathematicians, engineers, and operations research specialists will find this book stimulating, challenging, and an asset to their work. 1993 Statistics for Spatial Data, Revised Edition Noel Cressie, Iowa State University, USA Designed for the scientific and engineering professional eager to exploit its enormous potential, Statistics for Spatial Data is a primer to the theory as well as the nuts-and-bolts of this influential technique. Focusing on the three areas of geostatistical data, lattice data, and point patterns, the book sheds light on the link between data and model, and reveals how spatial statistical models can be used to solve a host of problems in science and engineering. The previous edition was hailed by Mathematical Reviews as "an excellent book which…will become a basic reference". Revised to reflect state-of-the-art developments, this edition also features many detailed examples, numerous illustrations, and over 1000 references. The first fully comprehensive introduction, Statistics for Spatial Data is an essential guide for professionals in biology, earth sciences, civil, electrical and agricultural engineering, geography, epidemiology, and ecology. 1993

Cooperative Control of Multi-Agent Systems: An Optimal and Robust Perspective reports and encourages technology transfer in the field of cooperative control of multi-agent systems. The book deals with UGVs, UAVs, UUVs and spacecraft, and more. It presents an extended exposition of the authors' recent work on all aspects of multi-agent technology. Modelling and cooperative control of multi-agent systems are topics of great interest, across both academia (research and education) and industry (for real applications and end-users). Graduate students and researchers from a wide spectrum of specialties in electrical, mechanical or aerospace engineering fields will use this book as a key resource.