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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.
Mathematical optimization. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis
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Operational research. Game theory --- Mathematical optimization --- 519.6 --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis
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The goal of this book is to report original researches on algorithms and applications of Tabu Search to real-world problems as well as recent improvements and extensions on its concepts and algorithms. The book’ Chapters identify useful new implementations and ways to integrate and apply the principles of Tabu Search, to hybrid it with others optimization methods, to prove new theoretical results, and to describe the successful application of optimization methods to real world problems. Chapters were selected after a careful review process by reviewers, based on the originality, relevance and their contribution to local search techniques and more precisely to Tabu Search.
Mathematical optimization. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Algorithms & data structures
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The symposium Operations Research 2007 was held from September 5-7, 2007 at the Saarland University in Saarbru ¨cken. This international conference is at the same time the annual meeting of the German - erations Research Society (GOR). The transition in Germany (and many other countries in Europe) from a production orientation to a service society combined with a continuous demographic change generated a need for intensi?ed Op- ations Research activities in this area. On that account this conference has been devoted to the role of Operations Research in the service industry. The links to Operations Research are manifold and include many di?erent topics which are particularly emphasized in scienti?c sections of OR 2007. More than 420 participants from 30 countries made this event very international and successful. The program consisted of three p- nary,elevensemi-plenaryandmorethan300contributedpresentations, which had been organized in 18 sections. During the conference, the GOR Dissertation and Diploma Prizes were awarded. We congratulate all winners, especially Professor Wolfgang Domschke from the Da- stadt University of Technology, on receiving the GOR Scienti?c Prize Award.
Operations research --- Operations research. --- Mathematical optimization. --- Operations Research/Decision Theory. --- Optimization. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Simulation methods --- System analysis --- Operational analysis --- Operational research --- Industrial engineering --- Management science --- Research --- System theory --- Decision making. --- Deciding --- Decision (Psychology) --- Decision analysis --- Decision processes --- Making decisions --- Management --- Management decisions --- Choice (Psychology) --- Problem solving --- Decision making
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This groundbreaking book extends traditional approaches of risk measurement and portfolio optimization by combining distributional models with risk or performance measures into one framework. Throughout these pages, the expert authors explain the fundamentals of probability metrics, outline new approaches to portfolio optimization, and discuss a variety of essential risk measures. Using numerous examples, they illustrate a range of applications to optimal portfolio choice and risk theory, as well as applications to the area of computational finance that may be useful to financial engineers.
Stochastic processes. --- Mathematical optimization. --- Risk assessment --- Portfolio management --- Mathematical models. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Random processes --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Probabilities --- Stochastic processes --- Mathematical optimization --- Mathematical models --- E-books --- Investment management
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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.
Medicine --- Mathematical optimization. --- Mathematics. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Medical mathematics --- Medicine. --- Radiology, Medical. --- Medicine/Public Health, general. --- Optimization. --- Calculus of Variations and Optimal Control; Optimization. --- Imaging / Radiology. --- Clinical radiology --- Radiology, Medical --- Radiology (Medicine) --- Medical physics --- Clinical sciences --- Medical profession --- Human biology --- Life sciences --- Medical sciences --- Pathology --- Physicians --- Health Workforce --- Calculus of variations. --- Radiology. --- Radiological physics --- Physics --- Radiation --- Isoperimetrical problems --- Variations, Calculus of
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This book presents the main methodological and theoretical developments in stochastic global optimization. The extensive text is divided into four chapters; the topics include the basic principles and methods of global random search, statistical inference in random search, Markovian and population-based random search methods, methods based on statistical models of multimodal functions and principles of rational decisions theory. Key features: * Inspires readers to explore various stochastic methods of global optimization by clearly explaining the main methodological principles and features of the methods; * Includes a comprehensive study of probabilistic and statistical models underlying the stochastic optimization algorithms; * Expands upon more sophisticated techniques including random and semi-random coverings, stratified sampling schemes, Markovian algorithms and population based algorithms; *Provides a thorough description of the methods based on statistical models of objective function; *Discusses criteria for evaluating efficiency of optimization algorithms and difficulties occurring in applied global optimization. Stochastic Global Optimization is intended for mature researchers and graduate students interested in global optimization, operations research, computer science, probability, statistics, computational and applied mathematics, mechanical and chemical engineering, and many other fields where methods of global optimization can be used.
Mathematical optimization. --- Stochastic processes. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Random processes --- Probabilities --- Distribution (Probability theory. --- Mathematical statistics. --- Optimization. --- Probability Theory and Stochastic Processes. --- Statistical Theory and Methods. --- Distribution functions --- Frequency distribution --- Characteristic functions --- Mathematics --- Statistical inference --- Statistics, Mathematical --- Statistics --- Sampling (Statistics) --- Statistical methods --- Probabilities. --- Statistics . --- Statistical analysis --- Statistical data --- Statistical science --- Econometrics --- Probability --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk
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This comprehensive work examines important recent developments and modern applications in the fields of optimization, control, game theory, and equilibrium programming. In particular, the concepts of equilibrium and optimality are of immense practical importance affecting decision-making problems regarding policy and strategies, and in understanding and predicting systems in different application domains, ranging from economics and engineering to military applications. The book consists of twenty-nine survey chapters written by distinguished researchers in the above areas.
Equilibrium (Economics) --- Game theory. --- Mathematical optimization. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Games, Theory of --- Theory of games --- Mathematical models --- Mathematics --- DGE (Economics) --- Disequilibrium (Economics) --- DSGE (Economics) --- Dynamic stochastic general equilibrium (Economics) --- Economic equilibrium --- General equilibrium (Economics) --- Partial equilibrium (Economics) --- SDGE (Economic theory) --- Economics --- Statics and dynamics (Social sciences) --- Mathematics. --- Optimization. --- Game Theory, Economics, Social and Behav. Sciences. --- Applications of Mathematics. --- Math --- Science --- Applied mathematics. --- Engineering mathematics. --- Engineering --- Engineering analysis
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From the reviews of the previous editions ".... The book is a first class textbook and seems to be indispensable for everybody who has to teach combinatorial optimization. It is very helpful for students, teachers, and researchers in this area. The author finds a striking synthesis of nice and interesting mathematical results and practical applications. ... the author pays much attention to the inclusion of well-chosen exercises. The reader does not remain helpless; solutions or at least hints are given in the appendix. Except for some small basic mathematical and algorithmic knowledge the book is self-contained. ..." K.Engel, Mathematical Reviews 2002 The substantial development effort of this text, involving multiple editions and trailing in the context of various workshops, university courses and seminar series, clearly shows through in this new edition with its clear writing, good organisation, comprehensive coverage of essential theory, and well-chosen applications. The proofs of important results and the representation of key algorithms in a Pascal-like notation allow this book to be used in a high-level undergraduate or low-level graduate course on graph theory, combinatorial optimization or computer science algorithms. The well-worked solutions to exercises are a real bonus for self study by students. The book is highly recommended. P .B. Gibbons, Zentralblatt für Mathematik 1061, 2005 The third edition of this standard textbook contains additional material: two new application sections (on graphical codes and their decoding) and about two dozen further exercises (with solutions, as throughout the text). Moreover, recent developments have been discussed and referenced, in particular for the travelling salesman problem. The presentation has been improved in many places (for instance, in the chapters on shortest paths and on colorings), and a number of proofs have been reorganized, making them more precise or more transparent.
Combinatorial optimization. --- Graph theory. --- Graph theory --- Graphs, Theory of --- Theory of graphs --- Combinatorial analysis --- Topology --- Optimization, Combinatorial --- Mathematical optimization --- Extremal problems --- Global analysis (Mathematics). --- Combinatorics. --- Mathematical optimization. --- Computer science. --- Analysis. --- Optimization. --- Mathematics of Computing. --- Informatics --- Science --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Combinatorics --- Algebra --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Mathematical analysis. --- Analysis (Mathematics). --- Computer science—Mathematics. --- 517.1 Mathematical analysis --- Combinatorial analysis.
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Computational models and methods are central to the analysis of economic and financial decisions. Simulation and optimisation are widely used as tools of analysis, modelling and testing. The focus of this book is the development of computational methods and analytical models in financial engineering that rely on computation. The book contains eighteen chapters written by leading researchers in the area on portfolio optimization and option pricing; estimation and classification; banking; risk and macroeconomic modelling. It explores and brings together current research tools and will be of interest to researchers, analysts and practitioners in policy and investment decisions in economics and finance. "This book collects frontier work by researchers in computational economics in a tribute to Manfred Gilli, a leading member of this community. Contributions cover many of the topics researched by Gilli during his career: portfolio optimization and option pricing, estimation and classification, as well as banking, risk and macroeconomic modeling. The editors have put together a remarkable panorama of the rapidly growing and diversifying field of computational economics and finance." Michel Juillard, Paris School of Economics and University Paris 8.
Financial engineering. --- Portfolio management --- Mathematical optimization. --- Risk assessment --- Mathematical models. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Computational finance --- Engineering, Financial --- Finance --- Public finance. --- Finance. --- Statistics. --- Macroeconomics. --- Public Economics. --- Finance, general. --- Quantitative Finance. --- Statistics for Business, Management, Economics, Finance, Insurance. --- Macroeconomics/Monetary Economics//Financial Economics. --- Economics --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Mathematics --- Econometrics --- Funding --- Funds --- Currency question --- Cameralistics --- Public finance --- Public finances --- Economics, Mathematical . --- Statistics . --- Mathematical economics --- Methodology
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