'Optimization Day' (OD) has been a series of annual mini-conferences in Aus tralia since 1994. The purpose of this series of events is to gather researchers in optimization and its related areas from Australia and their collaborators, in order to exchange new developments of optimization theories, methods and their applications. The first four OD mini-conferences were held in The Uni versity of Ballarat (1994), The University of New South Wales (1995), The University of Melbourne (1996) and Royal Melbourne Institute of Technology (1997), respectively. They were all on the eastern coast of Australia. The fifth mini-conference Optimization Days was held at the Centre for Ap plied Dynamics and Optimization (CADO), Department of Mathematics and Statistics, The University of Western Australia, Perth, from 29 to 30 June 1998. This is the first time the OD mini-conference has been held at the west ern coast of Australia. This fifth OD preceded the International Conference on Optimization: Techniques and Applications (ICOTA) held at Curtin Uni versity of Technology. Many participants attended both events. There were 28 participants in this year's mini-conference and 22 presentations in the mini conference. The presentations in this volume are refereed contributions based on papers presented at the fifth Optimization Days mini-conference. The volume is di vided into the following parts: Global Optimization, Nonsmooth Optimization, Optimization Methods and Applications."

This book opens new avenues in understanding mathematical models within the context of a transition economy. The exposition lays out the methods for combining different mathematical structures and tools to effectively build the next model that will accurately reflect real world economic processes. Mathematical modeling of weather phenomena allows us to forecast certain essential weather parameters without any possibility of changing them. By contrast, modeling of transition economies gives us the freedom to not only predict changes in important indexes of all types of economies, but also to influence them more effectively in the desired direction. Simply put: any economy, including a transitional one, can be controlled. This book is useful to anyone who wants to increase profits within their business, or improve the quality of their family life and the economic area they live in. It is beneficial for undergraduate and graduate students specializing in the fields of Economic Informatics, Economic Cybernetics, Applied Mathematics and Large Information Systems, as well as for professional economists, and employees of state planning and statistical organizations.

The International Conference on Health Care Systems Engineering (HCSE) provided a timely opportunity to discuss statistical analysis and operations management issues in health care delivery systems. The conference took place in Milan between May 22nd and 24th, 2013. Scientists and practitioners discussed new ideas, methods and technologies for improving the operation of health care organizations. The event and this resulting volume emphasize research in the field of health care systems engineering developed in close collaboration with clinicians. Topics applicable to researchers and practitioners include: hospital drug logistics, operating theatres, modelling and simulation in patient care and healthcare organizations, home care services.

Wim van der Linden was just given a lifetime achievement award by the National Council on Measurement in Education. There is no one more prominent in the area of educational testing.

There are hundreds of computer-based credentialing exams in areas such as accounting, real estate, nursing, and securities, as well as the well-known admissions exams for college, graduate school, medical school, and law school - there is great need on the theory of testing.

This book presents the statistical theory and practice behind constructing good tests e.g., how is the first test item selected, how are the next items selected, and when do you have enough items.

Optimization is a rich and thriving mathematical discipline. The theory underlying current computational optimization techniques grows ever more sophisticated. The powerful and elegant language of convex analysis unifies much of this theory. The aim of this book is to provide a concise, accessible account of convex analysis and its applications and extensions, for a broad audience. It can serve as a teaching text, at roughly the level of first year graduate students. While the main body of the text is self-contained, each section concludes with an often extensive set of optional exercises. The new edition adds material on semismooth optimization, as well as several new proofs that will make this book even more self-contained.

In this book a general topological construction of extension is proposed for problems of attainability in topological spaces under perturbation of a system of constraints. This construction is realized in a special class of generalized elements defined as finitely additive measures. A version of the method of programmed iterations is constructed. This version realizes multi-valued control quasistrategies, which guarantees the solution of the control problem that consists in guidance to a given set under observation of phase constraints.

Audience: The book will be of interest to researchers, and graduate students in the field of optimal control, mathematical systems theory, measure and integration, functional analysis, and general topology.

This superb new book is one of the first publications in recent years to provide a broad overview of this interdisciplinary field. Most of the book is written in a self contained manner, assuming only a general knowledge of statistical mechanics and basic probabilty theory . It provides the reader with a sound introduction to the field and to the analytical techniques necessary to follow its most recent developments

This book deals with decision making in environments of significant data un certainty, with particular emphasis on operations and production management applications. For such environments, we suggest the use of the robustness ap proach to decision making, which assumes inadequate knowledge of the decision maker about the random state of nature and develops a decision that hedges against the worst contingency that may arise. The main motivating factors for a decision maker to use the robustness approach are: * It does not ignore uncertainty and takes a proactive step in response to the fact that forecasted values of uncertain parameters will not occur in most environments; * It applies to decisions of unique, non-repetitive nature, which are common in many fast and dynamically changing environments; * It accounts for the risk averse nature of decision makers; and * It recognizes that even though decision environments are fraught with data uncertainties, decisions are evaluated ex post with the realized data. For all of the above reasons, robust decisions are dear to the heart of opera tional decision makers. This book takes a giant first step in presenting decision support tools and solution methods for generating robust decisions in a variety of interesting application environments. Robust Discrete Optimization is a comprehensive mathematical programming framework for robust decision making.

Nonsmooth energy functions govern phenomena which occur frequently in nature and in all areas of life. They constitute a fascinating subject in mathematics and permit the rational understanding of yet unsolved or partially solved questions in mechanics, engineering and economics. This is the first book to provide a complete and rigorous presentation of the quasidifferentiability approach to nonconvex, possibly nonsmooth, energy functions, of the derivation and study of the corresponding variational expressions in mechanics, engineering and economics, and of their numerical treatment. The new variational formulations derived are illustrated by many interesting numerical problems. The techniques presented will permit the reader to check any solution obtained by other heuristic techniques for nonconvex, nonsmooth energy problems. A civil, mechanical or aeronautical engineer can find in the book the only existing mathematically sound technique for the formulation and study of nonconvex, nonsmooth energy problems. Audience: The book will be of interest to pure and applied mathematicians, physicists, researchers in mechanics, civil, mechanical and aeronautical engineers, structural analysts and software developers. It is also suitable for graduate courses in nonlinear mechanics, nonsmooth analysis, applied optimization, control, calculus of variations and computational mechanics.

Invexity and Optimization presents results on invex function and their properties in smooth and nonsmooth cases, pseudolinearity and eta-pseudolinearity. Results on optimality and duality for a nonlinear scalar programming problem are presented, second and higher order duality results are given for a nonlinear scalar programming problem, and saddle point results are also presented. Invexity in multiobjective programming problems and Kuhn-Tucker optimality conditions are given for a multiobjecive programming problem, Wolfe and Mond-Weir type dual models are given for a multiobjective programming problem and usual duality results are presented in presence of invex functions. Continuous-time multiobjective problems are also discussed. Quadratic and fractional programming problems are given for invex functions. Symmetric duality results are also given for scalar and vector cases.

The theory of Vector Optimization is developed by a systematic usage of infimum and supremum. In order to get existence and appropriate properties of the infimum, the image space of the vector optimization problem is embedded into a larger space, which is a subset of the power set, in fact, the space of self-infimal sets. Based on this idea we establish solution concepts, existence and duality results and algorithms for the linear case. The main advantage of this approach is the high degree of analogy to corresponding results of Scalar Optimization. The concepts and results are used to explain and to improve practically relevant algorithms for linear vector optimization problems.

With contributions by specialists in optimization and practitioners in the fields of aerospace engineering, chemical engineering, and fluid and solid mechanics, the major themes include an assessment of the state of the art in optimization algorithms as well as challenging applications in design and control, in the areas of process engineering and systems with partial differential equation models.

This book deals with combinatorial aspects of epistasis, a notion that existed for years in genetics and appeared in the ?eld of evolutionary algorithms in the early 1990s. Even thoughthe?rst chapterputsepistasisintheperspective ofevolutionary algorithms and arti?cial intelligence, and applications occasionally pop up in other chapters, thisbookisessentiallyaboutmathematics, aboutcombinatorialtechniques to compute in an e?cient and mathematically elegant way what will be de?ned as normalized epistasis. Some of the material in this book ?nds its origin in the PhD theses of Hugo Van Hove [97] and Dominique Suys [95]. The sixth chapter also contains material that appeared in the dissertation of Luk Schoofs [84]. Together with that of M. Teresa Iglesias [36], these dissertations form the backbone of a decade of mathematical ventures in the world of epistasis. The authors wish to acknowledge support from the Flemish Fund of Scienti?c - search (FWO-Vlaanderen) and of the Xunta de Galicia. They also wish to explicitly mentiontheintellectualandmoralsupporttheyreceivedthroughoutthepreparation of this work from their family and their colleagues Emilio Villanueva, Jose Mar'a Barja and Arnold Beckelheimer, as well as our local T T Xpert Jan Adriaenssens.

In 1984, N. Karmarkar published a seminal paper on algorithmic linear programming. During the subsequent decade, it stimulated a huge outpouring of new algorithmic results by researchers world-wide in many areas of mathematical programming and numerical computation. This book gives an overview of the resulting, dramatic reorganization that has occurred in one of these areas: algorithmic differentiable optimization and equation-solving, or, more simply, algorithmic differentiable programming. The book is aimed at readers familiar with advanced calculus, numerical analysis, in particular numerical linear algebra, the theory and algorithms of linear and nonlinear programming, and the fundamentals of computer science, in particular, computer programming and the basic models of computation and complexity theory. J.L. Nazareth is a Professor in the Department of Pure and Applied Mathematics at Washington State University. He is the author of two books previously published by Springer-Verlag, DLP and Extensions: An Optimization Model and Decision Support System (2001) and The Newton-Cauchy Framework: A Unified Approach to Unconstrained Nonlinear Minimization (1994).

This book presents a new optimization flow for quantum circuits realization. At the reversible level, optimization algorithms are presented to reduce the quantum cost. Then, new mapping approaches to decompose reversible circuits to quantum circuits using different quantum libraries are described. Finally, optimization techniques to reduce the quantum cost or the delay are applied to the resulting quantum circuits. Furthermore, this book studies the complexity of reversible circuits and quantum circuits from a theoretical perspective.

Many advances have recently been made in metaheuristic methods, from theory to applications. The editors, both leading experts in this field, have assembled a team of researchers to contribute 21 chapters organized into parts on simulated annealing, tabu search, ant colony algorithms, general purpose studies of evolutionary algorithms, applications of evolutionary algorithms, and metaheuristics.

The focus of the present volume is stochastic optimization of dynamical systems in discrete time where - by concentrating on the role of information regarding optimization problems - it discusses the related discretization issues. There is a growing need to tackle uncertainty in applications of optimization. For example the massive introduction of renewable energies in power systems challenges traditional ways to manage them. This book lays out basic and advanced tools to handle and numerically solve such problems and thereby is building a bridge between Stochastic Programming and Stochastic Control. It is intended for graduates readers and scholars in optimization or stochastic control, as well as engineers with a background in applied mathematics.

The volume, devoted to variational analysis and its applications, collects selected and refereed contributions, which provide an outline of the field. The meeting of the title "Equilibrium Problems and Variational Models," which was held in Erice (Sicily) in the period June 23 - July 2 2000, was the occasion of the presentation of some of these papers; other results are a consequence of a fruitful and constructive atmosphere created during the meeting. New results, which enlarge the field of application of variational analysis, are presented in the book; they deal with the vectorial analysis, time dependent variational analysis, exact penalization, high order deriva tives, geometric aspects, distance functions and log-quadratic proximal methodology. The new theoretical results allow one to improve in a remarkable way the study of significant problems arising from the applied sciences, as continuum model of transportation, unilateral problems, multicriteria spatial price models, network equilibrium problems and many others. As noted in the previous book "Equilibrium Problems: Nonsmooth Optimization and Variational Inequality Models," edited by F. Giannessi, A. Maugeri and P.M. Pardalos, Kluwer Academic Publishers, Vol. 58 (2001), the progress obtained by variational analysis has permitted to han dle problems whose equilibrium conditions are not obtained by the mini mization of a functional. These problems obey a more realistic equilibrium condition expressed by a generalized orthogonality (complementarity) con dition, which enriches our knowledge of the equilibrium behaviour. Also this volume presents important examples of this formulation."

This book presents two natural generalizations of continuous mappings, namely usco and quasicontinuous mappings. The first class considers set-valued mappings, the second class relaxes the definition of continuity. Both these topological concepts stem naturally from basic mathematical considerations and have numerous applications that are covered in detail.

There has been much recent progress in approximation algorithms for nonconvex continuous and discrete problems from both a theoretical and a practical perspective. In discrete (or combinatorial) optimization many approaches have been developed recently that link the discrete universe to the continuous universe through geomet ric, analytic, and algebraic techniques. Such techniques include global optimization formulations, semidefinite programming, and spectral theory. As a result new ap proximate algorithms have been discovered and many new computational approaches have been developed. Similarly, for many continuous nonconvex optimization prob lems, new approximate algorithms have been developed based on semidefinite pro gramming and new randomization techniques. On the other hand, computational complexity, originating from the interactions between computer science and numeri cal optimization, is one of the major theories that have revolutionized the approach to solving optimization problems and to analyzing their intrinsic difficulty. The main focus of complexity is the study of whether existing algorithms are efficient for the solution of problems, and which problems are likely to be tractable. The quest for developing efficient algorithms leads also to elegant general approaches for solving optimization problems, and reveals surprising connections among problems and their solutions. A conference on Approximation and Complexity in Numerical Optimization: Con tinuous and Discrete Problems was held during February 28 to March 2, 1999 at the Center for Applied Optimization of the University of Florida."

In this edition, the scope and character of the monograph did not change with respect to the first edition. Taking into account the rapid development of the field, we have, however, considerably enlarged its contents. Chapter 4 includes two additional sections 4.4 and 4.6 on theory and algorithms of D.C. Programming. Chapter 7, on Decomposition Algorithms in Nonconvex Optimization, is completely new. Besides this, we added several exercises and corrected errors and misprints in the first edition. We are grateful for valuable suggestions and comments that we received from several colleagues. R. Horst, P.M. Pardalos and N.V. Thoai March 2000 Preface to the First Edition Many recent advances in science, economics and engineering rely on nu merical techniques for computing globally optimal solutions to corresponding optimization problems. Global optimization problems are extraordinarily di verse and they include economic modeling, fixed charges, finance, networks and transportation, databases and chip design, image processing, nuclear and mechanical design, chemical engineering design and control, molecular biology, and environment al engineering. Due to the existence of multiple local optima that differ from the global solution all these problems cannot be solved by classical nonlinear programming techniques. During the past three decades, however, many new theoretical, algorith mic, and computational contributions have helped to solve globally multi extreme problems arising from important practical applications."

Optimization is a serious issue, touching many aspects of our life and activity. But it has not yet been completely absorbed in our culture. In this book the authors point out how relatively young even the word "model" is. On top of that, the concept is rather elusive. How to deal with a technology that ?nds applicationsinthingsasdi?erentaslogistics,robotics,circuitlayout,?nancial deals and tra?c control? Although, during the last decades, we made signi?cant progress, the broad public remained largely unaware of that. The days of John von Neumann, with his vast halls full of people frantically working mechanical calculators are long gone. Things that looked completely impossible in my youth, like solving mixed integer problems are routine by now. All that was not just achieved by ever faster and cheaper computers, but also by serious progress in mathematics. But even in a world that more and more understands that it cannot a?ord to waste resources, optimization remains to a large extent unknown. R It is quite logical and also fortunate that SAP , the leading supplier of enterprise management systems has embedded an optimizer in his software. The authors have very carefully investigated the capabilities and the limits of APO. Remember that optimization is still a work in progress. We do not have the tool that does everything for everybody.

This book addresses stochastic optimization procedures in a broad manner. The first part offers an overview of relevant optimization philosophies; the second deals with benchmark problems in depth, by applying a selection of optimization procedures. Written primarily with scientists and students from the physical and engineering sciences in mind, this book addresses a larger community of all who wish to learn about stochastic optimization techniques and how to use them.