Support for addressing the on-going global changes needs solutions for new scientific problems which in turn require new concepts and tools. A key issue concerns a vast variety of irreducible uncertainties, including extreme events of high multidimensional consequences, e.g., the climate change. The dilemma is concerned with enormous costs versus massive uncertainties of extreme impacts. Traditional scientific approaches rely on real observations and experiments. Yet no sufficient observations exist for new problems, and "pure" experiments, and learning by doing may be expensive, dangerous, or impossible. In addition, the available historical observations are often contaminated by past actions, and policies. Thus, tools are presented for the explicit treatment of uncertainties using "synthetic" information composed of available "hard" data from historical observations, the results of possible experiments, and scientific facts, as well as "soft" data from experts' opinions, and scenarios.

The problem of stochastic control of partially observable systems plays an important role in many applications. All real problems are in fact of this type, and deterministic control as well as stochastic control with full observation can only be approximations to the real world. This justifies the importance of having a theory as complete as possible, which can be used for numerical implementation. This book first presents those problems under the linear theory that may be dealt with algebraically. Later chapters discuss the nonlinear filtering theory, in which the statistics are infinite dimensional and thus, approximations and perturbation methods are developed.

Optimization is concerned with finding the best (optimal) solution to mathematical problems that may arise in economics, engineering, the social sciences and the mathematical sciences. As is suggested by its title, this book surveys various ways of penetrating the subject. The author begins with a selection of the type of problem to which optimization can be applied and the remainder of the book develops the theory, mainly from the viewpoint of mathematical programming. To prevent the treatment becoming too abstract, subjects which may be considered 'unpractical' are not touched upon. The author gives plausible reasons, without forsaking rigor, to show how the subject develops 'naturally'. Professor Ponstein has provided a concise account of optimization which should be readily accessible to anyone with a basic understanding of topology and functional analysis. Advanced students and professionals concerned with operations research, optimal control and mathematical programming will welcome this useful and interesting book.

This volume is dedicated to the centenary of the outstanding mathematician of the 20th century, Sergey Sobolev, and, in a sense, to his celebrated work On a theorem of functional analysis, published in 1938, exactly 70 years ago, was where the original Sobolev inequality was proved. This double event is a good occasion to gather experts for presenting the latest results on the study of Sobolev inequalities, which play a fundamental role in analysis, the theory of partial differential equations, mathematical physics, and differential geometry. In particular, the following topics are discussed: Sobolev-type inequalities on manifolds and metric measure spaces, traces, inequalities with weights, unfamiliar settings of Sobolev type inequalities, Sobolev mappings between manifolds and vector spaces, properties of maximal functions in Sobolev spaces, the sharpness of constants in inequalities, etc.

The volume opens with a nice survey reminiscence, "My Love Affair with the Sobolev Inequality," by David R. Adams.

In the latter part of the twentieth century, the topic of generalizations of convexfunctions has attracted a sizable number of researchers,both in ma- ematics and in professional disciplines such as economics/management and engineering. In 1994 during the 15th International Symposium on Mathem- ical Programming in Ann Arbor, Michigan, I called together some colleagues to start an a?liation of researchers working in generalized convexity. The international Working Group of Generalized Convexity (WGGC) was born. Its website at www.genconv.org has been maintained by Riccardo Cambini, University of Pisa. Riccardo's father, Alberto Cambini, and Alberto's long-term colleague Laura Martein in the Faculty of Economics, University of Pisa, are the - authors of this volume. My own contact with generalized convexity in Italy datesbacktomy?rstvisittotheirdepartmentin1980,atatimewhenthe?rst international conference on generalized convexity was in preparation. Thirty years later it is now referred to as GC1, an NATO Summer School in V- couver, Canada. Currently WGGC is preparing GC9 which is to take place in Kaohsiung, Taiwan. As founding chair and also current chair of WGGC, I am delighted to see the continued interest in generalized convexity of functions, augmented by the topic of generalized monotonicity of maps. Eight international conferences have taken place in this research area, in North America (2), Europe (5) and Asia (1). We thought it was now time to return to Asia since our membership has shifted towards Asia. AsanappliedmathematicianIhavetaughtmostlyinmanagementschools.

Jon Lee focuses on key mathematical ideas leading to useful models and algorithms, rather than on data structures and implementation details, in this introductory graduate-level text for students of operations research, mathematics, and computer science. The viewpoint is polyhedral, and Lee also uses matroids as a unifying idea. Topics include linear and integer programming, polytopes, matroids and matroid optimization, shortest paths, and network flows. Problems and exercises are included throughout as well as references for further study.

Jon Lee focuses on key mathematical ideas leading to useful models and algorithms, rather than on data structures and implementation details, in this introductory graduate-level text for students of operations research, mathematics, and computer science. The viewpoint is polyhedral, and Lee also uses matroids as a unifying idea. Topics include linear and integer programming, polytopes, matroids and matroid optimization, shortest paths, and network flows. Problems and exercises are included throughout as well as references for further study.

Metaheuristics have been shown to be e?ective for di?cult combinatorial - timization problems appearing in various industrial, economical, and scienti?c domains. Prominent examples of metaheuristics are evolutionary algorithms, tabu search, simulated annealing, scatter search, memetic algorithms, variable neighborhood search, iterated local search, greedy randomized adaptive search procedures, ant colony optimization and estimation of distribution algorithms. Problems solved successfully include scheduling, timetabling, network design, transportation and distribution, vehicle routing, the travelling salesman pr- lem, packing and cutting, satis?ability and general mixed integer programming. EvoCOPbeganin2001andhasbeenheldannuallysincethen.Itwasthe?rst event speci?cally dedicated to the application of evolutionary computation and related methods to combinatorial optimization problems. Originally held as a workshop, EvoCOPbecameaconferencein2004.Theeventsgaveresearchersan excellent opportunity to present their latest research and to discuss current - velopments and applications. Following the general trend of hybrid metaheur- tics and diminishing boundaries between the di?erent classes of metaheuristics, EvoCOP has broadened its scope over the last years and invited submissions on any kind of metaheuristic for combinatorial optimization

This book revises the well-known capacity control problem in revenue management from the perspective of a risk-averse decision-maker. Modelling an expected utility maximizing decision maker, the problem is formulated as a risk-sensitive Markov decision process. Special emphasis is put on the existence of structured optimal policies. Numerical examples illustrate the results.

The Fifth International Conference on Automatic Differentiation held from August 11 to 15, 2008 in Bonn, Germany, is the most recent one in a series that began in Breckenridge, USA, in 1991 and continued in Santa Fe, USA, in 1996, Nice, France, in 2000 and Chicago, USA, in 2004. The 31 papers included in these proceedings re?ect the state of the art in automatic differentiation (AD) with respect to theory, applications, and tool development. Overall, 53 authors from institutions in 9 countries contributed, demonstrating the worldwide acceptance of AD technology in computational science. Recently it was shown that the problem underlying AD is indeed NP-hard, f- mally proving the inherently challenging nature of this technology. So, most likely, no deterministic "silver bullet" polynomial algorithm can be devised that delivers optimum performance for general codes. In this context, the exploitation of doma- speci?c structural information is a driving issue in advancing practical AD tool and algorithm development. This trend is prominently re?ected in many of the pub- cations in this volume, not only in a better understanding of the interplay of AD and certain mathematical paradigms, but in particular in the use of hierarchical AD approaches that judiciously employ general AD techniques in application-speci?c - gorithmic harnesses. In this context, the understanding of structures such as sparsity of derivatives, or generalizations of this concept like scarcity, plays a critical role, in particular for higher derivative computations.

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.

This book constitutes the refereed proceedings of the 7th European Conference on Evolutionary Computation in Combinatorial Optimization, EvoCOP 2007, held in Valencia, Spain in April 2007. The 21 revised full papers cover evolutionary algorithms as well as various other metaheuristics, like scatter search, tabu search, memetic algorithms, variable neighborhood search, ant colony optimization, and particle swarm optimization algorithms.

This book constitutes the refereed proceedings of the International Workshop on Engineering Stochastic Local Search Algorithms 2007, held in Brussels, Belgium, September 6-8, 2007.

The 12 revised full papers presented together with 9 short papers were carefully reviewed and selected from more than 50 submissions. The topics include Methodological developments, behavior of SLS algorithms, search space analysis, algorithm performance, tuning procedures, AI/OR techniques and dynamic behaviour.

This book constitutes the refereed proceedings of the First International Conference on Combinatorial Optimization and Applications, COCOA 2007, held in Xi'an, China in August 2007.

The 29 revised full papers presented together with 8 invited papers and 2 invited presentations were carefully reviewed and selected from 114 submissions. The papers feature original research in the areas of combinatorial optimization - both theoretical issues and and applications motivated by real-world problems thus showing convincingly the usefulness and efficiency of the algorithms discussed in a practical setting.

Combinatorial optimization and in particular the great variety of fascinating problemsthatbelong to thisareahaveattractedmanyresearchersformorethan halfacentury.Duetothepracticalrelevanceofsolvinghardreal-worldproblems, much research e?ort has been devoted to the development of heuristic methods aimed at ?nding good approximate solutions in a reasonable computation time. Some solution paradigms that are not speci?c for one particular problem have been deeply studied in the past, and the term metaheuristic is now common for such optimization heuristics. Several metaheuristics - simulated annealing, - netic and evolutionary algorithms, tabu search, ant colony optimization, scatter search, iterated local search, and greedy randomized adaptive search procedures beingsomeofthem-havefoundtheirownresearchcommunities, andspecialized conferences devoted to such techniques have been organized. Plenty of classical hard problems, such as the quadratic assignment pr- lem, the traveling salesman problem, problems in vehicle routing, scheduling, and timetabling, etc., have been tackled successfully with metaheuristic - proaches. Several thereof are currently considered state-of-the-art methods for solving such problems. However, for many years the main focus of research was on the application of single metaheuristics to given problems. A tendency to compare di?erent metaheuristics against each other could be observed, and sometimes this competition led to thinking in stereotypes in the research communities

This book constitutes the refereed proceedings of the 6th European Conference on Evolutionary Computation in Combinatorial Optimization, EvoCOP 2006, held in Budapest, Hungary in April 2006. The 24 revised full papers presented were carefully reviewed and selected from 77 submissions. The papers include coverage of evolutionary algorithms as well as various other metaheuristics, like scatter search, tabu search, and memetic algorithms.

Critical regimes of two-phase flows with a polydisperse solid phase form the basis of such widespread industrial processes as separation of various powdery materials and minerals dressing. It is impossible to describe such complicated flows analytically. Therefore, this study concentrates on invariants experimentally revealed and theoretically grounded for such flows.

This approach can be compared with the situation in gases, where in order to determine principal parameters of their state, one does not need to measure the kinetic energy and velocity of each molecule and find its contribution to the temperature and pressure. These parameters are determined in a simple way for the system on the whole.

A novel conception of two-phase flows allowing the formulation of their statistical parameters is physically substantiated. On the basis of the invariants and these parameters, a comprehensive method of estimating and predicting mass transfer in such flows is developed.

It is noteworthy that the presented results are mostly phenomenological. Such an approach can be successfully extended to the separation of liquids, gases and isotopes.

The book is intended for students and specialists engaged in chemical technology, mineral dressing, ceramics, microelectronics, pharmacology, power generation, thermal engineering and other fields in which flows carrying solid particles are used in the technological process.

Problems demanding globally optimal solutions are ubiquitous, yet many are intractable when they involve constrained functions having many local optima and interacting, mixed-type variables.

The differential evolution (DE) algorithm is a practical approach to global numerical optimization which is easy to understand, simple to implement, reliable, and fast. Packed with illustrations, computer code, new insights, and practical advice, this volume explores DE in both principle and practice. It is a valuable resource for professionals needing a proven optimizer and for students wanting an evolutionary perspective on global numerical optimization.

A companion CD includes DE-based optimization software in several programming languages.

1 With its fourth edition, the ANTS series of workshops has changed its name. Theoriginal"ANTS-FromAntColoniestoArti?cialAnts: InternationalWo- shop on Ant Algorithms" has become "ANTS - International Workshop on Ant Colony Optimization and Swarm Intelligence." This change is mainly due to the following reasons. First, the term "ant algorithms" was slower in spreading in the research community than the term "swarm intelligence," while at the sametime research inso-calledswarm robotics wasthesubjectofincreasingactivity: itwastherefore an obvious choice to substitute the term ant algorithms with the more accepted and used term swarm intelligence. Second, although swarm intelligence research has undoubtedly produced a 2 number of interesting and promising research directions, we think it is fair to say that its most successful strand is the one known as "ant colony optimi- tion."Ant colony optimization, ?rst introducedin the early1990sasa noveltool fortheapproximatesolutionofdiscreteoptimizationproblems, hasrecentlyseen an explosion in the number of its applications, both to academic and real-world problems, and is currently being extended to the realm of continuous optimi- tion (a few papers on this subject being published in these proceedings). It is therefore a reasonable choice to have the term ant colony optimization as part of the workshop name.

This book presents basic optimization principles and gradient-based algorithms to a general audience in a brief and easy-to-read form, without neglecting rigor. The work should enable professionals to apply optimization theory and algorithms to their own particular practical fields of interest, be it engineering, physics, chemistry, or business economics. Most importantly, for the first time in a relatively brief and introductory work, due attention is paid to the difficulties - such as noise, discontinuities, expense of function evaluations, and the existence of multiple minima - that often unnecessarily inhibit the use of gradient-based methods. In a separate chapter on new gradient-based methods developed by the author and his coworkers, it is shown how these difficulties may be overcome without losing the desirable features of classical gradient-based methods.

This volume contains the Proceedings of the Twelfth French-German-Spanish Conference on Optimization held at the University of Avignon in 2004. We refer to this conference by using the acronym FGS-2004. During the period September 20-24, 2004, about 180 scientists from around the world met at Avignon (France) to discuss recent developments in optimization and related fields. The main topics discussed during this meeting were the following: 1. smooth and nonsmooth continuous optimization problems, 2. numerical methods for mathematical programming, 3. optimal control and calculus of variations, 4. differential inclusions and set-valued analysis, 5. stochastic optimization, 6. multicriteria optimization, 7. game theory and equilibrium concepts, 8. optimization models in finance and mathematical economics, 9. optimization techniques for industrial applications. The Scientific Committee of the conference consisted of F. Bonnans (Rocqu- court, France), J.-B. Hiriart-Urruty (Toulouse, France), F. Jarre (Diisseldorf, Germany), M.A. Lopez (Alicante, Spain), J.E. Martinez-Legaz (Barcelona, Spain), H. Maurer (Miinster, Germany), S. Pickenhain (Cottbus, Germany), A. Seeger (Avignon, France), and M. Thera (Limoges, France). The conference FGS-2004 is the 12th of the series of French-German meetings which started in Oberwolfach in 1980 and was continued in Confolant (1981), Luminy (1984), Irsee (1986), Varetz (1988), Lambrecht (1991), Dijon (1994), Trier (1996), Namur (1998), Montpellier (2000), and Cottbus (2002).

Optimization is the art, science and mathematics of finding the "best" member of a finite or infinite set of possible choices, based on some objective measure of the merit of each choice in the set. Three key facets of the subject are:

- the construction of optimization models that capture the range of available choices within a feasible set and the measure-of-merit of any particular choice in a feasible set relative to its competitors;

- the invention and implementation of efficient algorithms for solving optimization models;

- a mathematical principle of duality that relates optimization models to one another in a fundamental way. Duality cuts across the entire field of optimization and is useful, in particular, for identifying optimality conditions, i.e., criteria that a given member of a feasible set must satisfy in order to be an optimal solution.

This booklet provides a gentle introduction to the above topics and will be of interest to college students taking an introductory course in optimization, high school students beginning their studies in mathematics and science, the general reader looking for an overall sense of the field of optimization, and specialists in optimization interested in developing new ways of teaching the subject to their students.

John Lawrence Nazareth is Professor Emeritus in the Department of Mathematics at Washington State University and Affiliate Professor in the Department of Applied Mathematics at the University of Washington. He is the author of two recent books also published by Springer-Verlag which explore the above topics in more depth, Differentiable Optimization and Equation Solving (2003) and DLP andExtensions: An Optimization Model and Decision Support System (2001).

Evolutionary Computation (EC) involves the study of problem solving and op- mization techniques inspired by principles of natural evolution and genetics. EC has been able to draw the attention of an increasing number of researchers and practitioners in several ?elds. Evolutionary algorithms have in particular been showntobee?ectivefordi?cultcombinatorialoptimizationproblemsappearing in various industrial, economic, and scienti?c domains. This volume contains the proceedings of EvoCOP 2004, the 4th European ConferenceonEvolutionaryComputationinCombinatorialOptimization.Itwas held in Coimbra, Portugal, on April 5 7, 2004, jointly with EuroGP 2004, the 7th European Conference on Genetic Programming, and EvoWorkshops 2004, which consisted of the following six individual workshops: EvoBIO, the 2nd - ropean Workshop on Evolutionary Bioinformatics; EvoCOMNET, the 1st - ropean Workshop on Evolutionary Computation in Communications, Networks, and Connected Systems; EvoHOT, the 1st European Workshop on Hardware Optimisation; EvoIASP, the 6th European Workshop on Evolutionary Com- tation in Image Analysis and Signal Processing; EvoMUSART, the 2nd Eu- pean Workshop on Evolutionary Music and Art; and EvoSTOC, the 1st Eu- pean Workshop on Evolutionary Algorithms in Stochastic and Dynamic En- ronments."

This volume contains a selection of papers referring to lectures presented at the symposium "Operations Research 2004" (OR 2004) held at Tilburg University, September 1-3, 2004. This international conference took place under the auspices of the German Operations Research Society (GOR) and the Dutch Operations Research Society (NGB).

The symposium had about 500 participants from countries all over the world. It attracted academics and practitioners working in various fields of Operations Research and provided them with the most recent advances in Operations Research and related areas in Economics, Mathematics, and Computer Science.

The program consisted of 4 plenary and 19 semi-plenary talks and more than 300 contributed presentations selected by the program committee to be presented in 20 sections.

A large number of real-life optimisation problems can only be realistically modelled with several~often conflicting~objectives. This fact requires us to abandon the concept of "optimal solution" in favour of vector optimization notions dealing with "efficient solution" and "efficient set". To solve these challenging multiobjective problems, the metaheuristics community has put forward a number of techniques commonly referred to as multiobjective meta- heuristics (MOMH). By its very nature, the field of MOMH covers a large research area both in terms of the types of problems solved and the techniques used to solve these problems. Its theoretical interest and practical applicability have attracted a large number of researchers and generated numerous papers, books and spe- cial issues. Moreover, several conferences and workshops have been organised, often specialising in specific sub-areas such as multiobjective evolutionary op- timisation. The main purpose of this volume is to provide an overview of the current state-of-the-art in the research field of MOMH. This overview is necessar- ily non-exhaustive, and contains both methodological and problem-oriented contributions, and applications of both population-based and neighbourhood- based heuristics. This volume originated from the workshop on multiobjective metaheuristics that was organised at the Carre des Sciences in Paris on November 4-5, 2002. This meeting was a joint effort of two working groups: ED jME and PM20.