Download or read book Optimisation a deux niveaux conditions d optimalite approximation et stabilite written by Smaïl Addoune and published by . This book was released on 1994 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Optimisation deux niveaux written by Smaïl Addoune and published by . This book was released on 1994 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: Notre travail s'est principalement orienté sur une analyse théorique de problèmes d'optimisation à deux niveaux avec une étude d'approximations de problèmes de Stackelberg susceptible de servir de base à des méthodes non heuristiques liées au développement de techniques d'optimisation globale. Dans le chapitre on présente des généralités sur les problèmes d'optimisation à deux niveaux. On donne des exemples permettant de motiver les différentes formulations proposées dans la littérature. L'analyse de la complexité des problèmes d'optimisation à deux niveaux est effectué dans le cas linéaire. Pour cela, on énonce un résultat établi par j. F. Bard que l'on démontre sous des hypothèses plus faibles et de façon plus directe. Le chapitre se termine par la présentation de résultats d'existence. Dans le deuxième chapitre, on s'intéresse à l'étude de conditions nécessaires et suffisantes d'optimalité pour des problèmes d'optimisation à deux niveaux à formulation forte. Dans un premier temps, on commence par l'étude d'une classe de problèmes d'optimisation globale appelés problèmes anti-convexes. On montre ensuite que certains problèmes d'optimisation à deux niveaux peuvent être reformulés en problèmes de la classe ainsi considérée, ce qui nous permet d'en déduire des conditions nécessaires et suffisantes d'optimalité locale. Pour les conditions d'optimalité globale on ne considère que le cas linéaire et on montre que le problème d'optimisation à deux niveaux est équivalent à un problème de maximisation d'une fonction convexe sur un convexe compact. Dans le dernier chapitre, on s'intéresse à des problèmes d'optimisation à deux niveaux à formulation faible. Pour de tels problèmes, il est connu qu'en général les solutions n'existent pas même sous des hypothèses assez fortes, ce qui a conduit à l'introduction d'ensembles de solutions plus grands qui peuvent constituer de bons candidats pour la résolution du problème pose. On étudie ensuite deux procédures de régularisation combinées à une méthode introduite par Molodtsov. Nous présentons alors des résultats nouveaux sur l'approximation de sous-équilibres exacts. Nous donnons pour terminer des résultats de stabilité sous perturbations de données
Download or read book Bilevel Optimization written by Stephan Dempe and published by Springer Nature. This book was released on 2020-11-23 with total page 679 pages. Available in PDF, EPUB and Kindle. Book excerpt: 2019 marked the 85th anniversary of Heinrich Freiherr von Stackelberg’s habilitation thesis “Marktform und Gleichgewicht,” which formed the roots of bilevel optimization. Research on the topic has grown tremendously since its introduction in the field of mathematical optimization. Besides the substantial advances that have been made from the perspective of game theory, many sub-fields of bilevel optimization have emerged concerning optimal control, multiobjective optimization, energy and electricity markets, management science, security and many more. Each chapter of this book covers a specific aspect of bilevel optimization that has grown significantly or holds great potential to grow, and was written by top experts in the corresponding area. In other words, unlike other works on the subject, this book consists of surveys of different topics on bilevel optimization. Hence, it can serve as a point of departure for students and researchers beginning their research journey or pursuing related projects. It also provides a unique opportunity for experienced researchers in the field to learn about the progress made so far and directions that warrant further investigation. All chapters have been peer-reviewed by experts on mathematical optimization.
Download or read book Approximation et optimisation written by Pierre Jean Laurent and published by . This book was released on 1972 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt: Au point de vue mathématique, l'objet de la théorie de l'optimisation est essentiellement d'étudier sous tous ses aspects la minimisation d'une fonction numérique (fonctionnelle) sur un domaine (défini en général par des « contraintes »). Dans la théorie de l'approximation cette fonction numérique a une forme particulière : elle provient d'une norme ou d'une semi-norme. L'un des buts essentiels de ce livre est d'étudier d'un point de vue unifié ces deux théories et de dégager les particularités de la seconde. Nous avons insisté tout parti- culièrement sur les théorèmes de caractérisation des solutions et dans la seconde partie sur la dualité. A quelques exceptions près, nous avons étudié exclusivement des problèmes d'optimisation convexe.
Download or read book Multistage Stochastic Optimization written by Georg Ch. Pflug and published by Springer. This book was released on 2014-11-12 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multistage stochastic optimization problems appear in many ways in finance, insurance, energy production and trading, logistics and transportation, among other areas. They describe decision situations under uncertainty and with a longer planning horizon. This book contains a comprehensive treatment of today’s state of the art in multistage stochastic optimization. It covers the mathematical backgrounds of approximation theory as well as numerous practical algorithms and examples for the generation and handling of scenario trees. A special emphasis is put on estimation and bounding of the modeling error using novel distance concepts, on time consistency and the role of model ambiguity in the decision process. An extensive treatment of examples from electricity production, asset liability management and inventory control concludes the book.
Download or read book Alternative Methods of Regression written by David Birkes and published by John Wiley & Sons. This book was released on 2011-09-20 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: Of related interest. Nonlinear Regression Analysis and its Applications Douglas M. Bates and Donald G. Watts ".an extraordinary presentation of concepts and methods concerning the use and analysis of nonlinear regression models.highly recommend[ed].for anyone needing to use and/or understand issues concerning the analysis of nonlinear regression models." --Technometrics This book provides a balance between theory and practice supported by extensive displays of instructive geometrical constructs. Numerous in-depth case studies illustrate the use of nonlinear regression analysis--with all data sets real. Topics include: multi-response parameter estimation; models defined by systems of differential equations; and improved methods for presenting inferential results of nonlinear analysis. 1988 (0-471-81643-4) 365 pp. Nonlinear Regression G. A. F. Seber and C. J. Wild ".[a] comprehensive and scholarly work.impressively thorough with attention given to every aspect of the modeling process." --Short Book Reviews of the International Statistical Institute In this introduction to nonlinear modeling, the authors examine a wide range of estimation techniques including least squares, quasi-likelihood, and Bayesian methods, and discuss some of the problems associated with estimation. The book presents new and important material relating to the concept of curvature and its growing role in statistical inference. It also covers three useful classes of models --growth, compartmental, and multiphase --and emphasizes the limitations involved in fitting these models. Packed with examples and graphs, it offers statisticians, statistical consultants, and statistically oriented research scientists up-to-date access to their fields. 1989 (0-471-61760-1) 768 pp. Mathematical Programming in Statistics T. S. Arthanari and Yadolah Dodge "The authors have achieved their stated intention.in an outstanding and useful manner for both students and researchers.Contains a superb synthesis of references linked to the special topics and formulations by a succinct set of bibliographical notes.Should be in the hands of all system analysts and computer system architects." --Computing Reviews This unique book brings together most of the available results on applications of mathematical programming in statistics, and also develops the necessary statistical and programming theory and methods. 1981 (0-471-08073-X) 413 pp.
Download or read book Chemical Product Design written by E. L. Cussler and published by Cambridge University Press. This book was released on 2001-04-16 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: Until recently, the chemical industry has been dominated by the manufacture of bulk commodity chemicals such as benzene, ammonia, and polypropylene. However, over the last decade a significant shift occurred. Now most chemical companies devote any new resources to the design and manufacture of specialty, high value-added chemical products such as pharmaceuticals, cosmetics, and electronic coatings. Although the jobs held by chemical engineers have also changed to reflect this altered business, their training has remained static, emphasizing traditional commodities. This ground-breaking text starts to redress the balance between commodities and higher value-added products. It expands the scope of chemical engineering design to encompass both process design and product design. The authors use a four-step procedure for chemical product design - needs, ideas, selection, manufacture - drawing numerous examples from industry to illustrate the discussion. The book concludes with a brief review of the economic issues. Chemical engineering students and beginning chemical engineers will find this text an inviting introduction to chemical product design.
Download or read book Statistical Inference for Ergodic Diffusion Processes written by Yury A. Kutoyants and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 493 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first book in inference for stochastic processes from a statistical, rather than a probabilistic, perspective. It provides a systematic exposition of theoretical results from over ten years of mathematical literature and presents, for the first time in book form, many new techniques and approaches.
Download or read book Semiparametric Theory and Missing Data written by Anastasios Tsiatis and published by Springer Science & Business Media. This book was released on 2007-01-15 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book summarizes current knowledge regarding the theory of estimation for semiparametric models with missing data, in an organized and comprehensive manner. It starts with the study of semiparametric methods when there are no missing data. The description of the theory of estimation for semiparametric models is both rigorous and intuitive, relying on geometric ideas to reinforce the intuition and understanding of the theory. These methods are then applied to problems with missing, censored, and coarsened data with the goal of deriving estimators that are as robust and efficient as possible.
Download or read book The Inverse Problem of the Calculus of Variations written by Dmitry V. Zenkov and published by Springer. This book was released on 2015-10-15 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of the present book is to give a systematic treatment of the inverse problem of the calculus of variations, i.e. how to recognize whether a system of differential equations can be treated as a system for extremals of a variational functional (the Euler-Lagrange equations), using contemporary geometric methods. Selected applications in geometry, physics, optimal control, and general relativity are also considered. The book includes the following chapters: - Helmholtz conditions and the method of controlled Lagrangians (Bloch, Krupka, Zenkov) - The Sonin-Douglas's problem (Krupka) - Inverse variational problem and symmetry in action: The Ostrogradskyj relativistic third order dynamics (Matsyuk.) - Source forms and their variational completion (Voicu) - First-order variational sequences and the inverse problem of the calculus of variations (Urban, Volna) - The inverse problem of the calculus of variations on Grassmann fibrations (Urban).
Download or read book Symmetry written by Hermann Weyl and published by Princeton University Press. This book was released on 2015-07-06 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: Symmetry is a classic study of symmetry in mathematics, the sciences, nature, and art from one of the twentieth century's greatest mathematicians. Hermann Weyl explores the concept of symmetry beginning with the idea that it represents a harmony of proportions, and gradually departs to examine its more abstract varieties and manifestations—as bilateral, translatory, rotational, ornamental, and crystallographic. Weyl investigates the general abstract mathematical idea underlying all these special forms, using a wealth of illustrations as support. Symmetry is a work of seminal relevance that explores the great variety of applications and importance of symmetry.
Download or read book Bilevel Programming Problems written by Stephan Dempe and published by Springer. This book was released on 2015-01-28 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes recent theoretical findings relevant to bilevel programming in general, and in mixed-integer bilevel programming in particular. It describes recent applications in energy problems, such as the stochastic bilevel optimization approaches used in the natural gas industry. New algorithms for solving linear and mixed-integer bilevel programming problems are presented and explained.
Download or read book Handbook of Nonlinear Partial Differential Equations written by Andrei D. Polyanin and published by CRC Press. This book was released on 2004-06-02 with total page 835 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook of Nonlinear Partial Differential Equations is the latest in a series of acclaimed handbooks by these authors and presents exact solutions of more than 1600 nonlinear equations encountered in science and engineering--many more than any other book available. The equations include those of parabolic, hyperbolic, elliptic and other types, and the authors pay special attention to equations of general form that involve arbitrary functions. A supplement at the end of the book discusses the classical and new methods for constructing exact solutions to nonlinear equations. To accommodate different mathematical backgrounds, the authors avoid wherever possible the use of special terminology, outline some of the methods in a schematic, simplified manner, and arrange the equations in increasing order of complexity. Highlights of the Handbook:
Download or read book Introduction to Nonsmooth Optimization written by Adil Bagirov and published by Springer. This book was released on 2014-08-12 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first easy-to-read text on nonsmooth optimization (NSO, not necessarily differentiable optimization). Solving these kinds of problems plays a critical role in many industrial applications and real-world modeling systems, for example in the context of image denoising, optimal control, neural network training, data mining, economics and computational chemistry and physics. The book covers both the theory and the numerical methods used in NSO and provide an overview of different problems arising in the field. It is organized into three parts: 1. convex and nonconvex analysis and the theory of NSO; 2. test problems and practical applications; 3. a guide to NSO software. The book is ideal for anyone teaching or attending NSO courses. As an accessible introduction to the field, it is also well suited as an independent learning guide for practitioners already familiar with the basics of optimization.
Download or read book Mathematics of the Decision Sciences written by George Bernard Dantzig and published by American Mathematical Soc.. This book was released on 1968-12-31 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Nonsmooth Optimization written by Claude Lemarechal and published by Elsevier. This book was released on 2014-05-19 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonsmooth Optimization contains the proceedings of a workshop on non-smooth optimization (NSO) held from March 28 to April 8,1977 in Austria under the auspices of the International Institute for Applied Systems Analysis. The papers explore the techniques and theory of NSO and cover topics ranging from systems of inequalities to smooth approximation of non-smooth functions, as well as quadratic programming and line searches. Comprised of nine chapters, this volume begins with a survey of Soviet research on subgradient optimization carried out since 1962, followed by a discussion on rates of convergence in subgradient optimization. The reader is then introduced to the method of subgradient optimization in an abstract setting and the minimal hypotheses required to ensure convergence; NSO and nonlinear programming; and bundle methods in NSO. A feasible descent algorithm for linearly constrained least squares problems is described. The book also considers sufficient minimization of piecewise-linear univariate functions before concluding with a description of the method of parametric decomposition in mathematical programming. This monograph will be of interest to mathematicians and mathematics students.
Download or read book Fixed Point Theorems with Applications to Economics and Game Theory written by Kim C. Border and published by Cambridge University Press. This book was released on 1985 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores fixed point theorems and its uses in economics, co-operative and noncooperative games.
