Optimality And Efficiency
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Author | : Panos M. Pardalos |
Publisher | : Springer Science & Business Media |
Total Pages | : 872 |
Release | : 2008-07-02 |
Genre | : Mathematics |
ISBN | : 0387772472 |
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 29 survey chapters written by distinguished researchers in the above areas.
Author | : Aharon Ben-Tal |
Publisher | : Princeton University Press |
Total Pages | : 565 |
Release | : 2009-08-10 |
Genre | : Mathematics |
ISBN | : 1400831059 |
Robust optimization is still a relatively new approach to optimization problems affected by uncertainty, but it has already proved so useful in real applications that it is difficult to tackle such problems today without considering this powerful methodology. Written by the principal developers of robust optimization, and describing the main achievements of a decade of research, this is the first book to provide a comprehensive and up-to-date account of the subject. Robust optimization is designed to meet some major challenges associated with uncertainty-affected optimization problems: to operate under lack of full information on the nature of uncertainty; to model the problem in a form that can be solved efficiently; and to provide guarantees about the performance of the solution. The book starts with a relatively simple treatment of uncertain linear programming, proceeding with a deep analysis of the interconnections between the construction of appropriate uncertainty sets and the classical chance constraints (probabilistic) approach. It then develops the robust optimization theory for uncertain conic quadratic and semidefinite optimization problems and dynamic (multistage) problems. The theory is supported by numerous examples and computational illustrations. An essential book for anyone working on optimization and decision making under uncertainty, Robust Optimization also makes an ideal graduate textbook on the subject.
Author | : Deen K. Chatterjee |
Publisher | : |
Total Pages | : |
Release | : 2011 |
Genre | : Electronic books |
ISBN | : 9781784027018 |
The Encyclopedia is an international, interdisciplinary, and collaborative project, spanning all the relevant areas of scholarship related to issues of global justice, and edited and advised by leading scholars from around the world. The wide-ranging entries present the latest ideas on this complex subject by authors who are at the cutting edge of inquiry.
Author | : Steven Hecht Orzack |
Publisher | : Cambridge University Press |
Total Pages | : 424 |
Release | : 2001-06-04 |
Genre | : Philosophy |
ISBN | : 9780521598361 |
These essays are intended to provide useful advice to "biologists in the trenches" but also to assess the larger theoretical and conceptual issues that form the basis of the current controversy." "This volume will serve to substantially advance the debate over adaptationism. It will be of interest to biologists, philosophers and historians of biology, anthropologists, psychologists, and cognitive scientists."--BOOK JACKET.
Author | : Aram Arutyunov |
Publisher | : Springer Science & Business Media |
Total Pages | : 318 |
Release | : 2000-10-31 |
Genre | : Mathematics |
ISBN | : 9780792366553 |
This book is devoted to one of the main questions of the theory of extremal problems, namely, to necessary and sufficient extremality conditions. The book consists of four parts. First, the abstract minimization problem with constraints is studied. The next chapter is devoted to one of the most important classes of extremal problems, the optimal control problem. Next, one of the main objects of the calculus of variations is studied, the integral quadratic form. Finally, local properties of smooth nonlinear mappings in a neighborhood of an abnormal point will be discussed. Audience: The book is intended for researchers interested in optimization problems. The book may also be useful for advanced students and postgraduate students.
Author | : Masatoshi Sakawa |
Publisher | : Springer Science & Business Media |
Total Pages | : 319 |
Release | : 2013-11-21 |
Genre | : Mathematics |
ISBN | : 1489916334 |
The main characteristics of the real-world decision-making problems facing humans today are multidimensional and have multiple objectives including eco nomic, environmental, social, and technical ones. Hence, it seems natural that the consideration of many objectives in the actual decision-making process re quires multiobjective approaches rather than single-objective. One ofthe major systems-analytic multiobjective approaches to decision-making under constraints is multiobjective optimization as a generalization of traditional single-objective optimization. Although multiobjective optimization problems differ from single objective optimization problems only in the plurality of objective functions, it is significant to realize that multiple objectives are often noncom mensurable and conflict with each other in multiobjective optimization problems. With this ob servation, in multiobjective optimization, the notion of Pareto optimality or effi ciency has been introduced instead of the optimality concept for single-objective optimization. However, decisions with Pareto optimality or efficiency are not uniquely determined; the final decision must be selected from among the set of Pareto optimal or efficient solutions. Therefore, the question is, how does one find the preferred point as a compromise or satisficing solution with rational pro cedure? This is the starting point of multiobjective optimization. To be more specific, the aim is to determine how one derives a compromise or satisficing so lution of a decision maker (DM), which well represents the subjective judgments, from a Pareto optimal or an efficient solution set.
Author | : Kirti R. Shah |
Publisher | : Springer Science & Business Media |
Total Pages | : 179 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461236622 |
There has been an enormous growth in recent years in the literature on discrete optimal designs. The optimality problems have been formulated in various models arising in the experimental designs and substantial progress has been made towards solving some of these. The subject has now reached a stage of completeness which calls for a self-contained monograph on this topic. The aim of this monograph is to present the state of the art and to focus on more recent advances in this rapidly developing area. We start with a discussion of statistical optimality criteria in Chapter One. Chapters Two and Three deal with optimal block designs. Row-column designs are dealt with in Chapter Four. In Chapter Five we deal with optimal designs with mixed effects models. Repeated measurement designs are considered in Chapter Six. Chapter Seven deals with some special situations and Weighing designs are dis cussed in Chapter Eight. We have endeavoured to include all the major developments that have taken place in the last three decades. The book should be of use to research workers in several areas including combinatorics as well as to the experimenters in diverse fields of applications. Since the details of the construction of the designs are available in excellent books, we have only pointed out the designs which have optimality proper ties. We believe, this will be adequate for the experimenters.
Author | : Friedrich Pukelsheim |
Publisher | : SIAM |
Total Pages | : 527 |
Release | : 2006-04-01 |
Genre | : Mathematics |
ISBN | : 0898716047 |
Optimal Design of Experiments offers a rare blend of linear algebra, convex analysis, and statistics. The optimal design for statistical experiments is first formulated as a concave matrix optimization problem. Using tools from convex analysis, the problem is solved generally for a wide class of optimality criteria such as D-, A-, or E-optimality. The book then offers a complementary approach that calls for the study of the symmetry properties of the design problem, exploiting such notions as matrix majorization and the Kiefer matrix ordering. The results are illustrated with optimal designs for polynomial fit models, Bayes designs, balanced incomplete block designs, exchangeable designs on the cube, rotatable designs on the sphere, and many other examples.
Author | : Mukul Majumdar |
Publisher | : World Scientific |
Total Pages | : 331 |
Release | : 2020 |
Genre | : Nonrenewable natural resources |
ISBN | : 9811210217 |
Introduction -- Evolution, extinction and sustainability -- Optimal harvesting: finite horizon -- Rolling plans: efficiency and long-run optimality -- Infinite horizon models: discounting and sustainability -- Profit maximization and extinction -- Utilization of an exhaustible resource: a partial equilibrium approach -- Production with an exhaustible resource: efficiency and intergenerational equity -- A Cobb-Douglas economy -- Technological transition: an optimistic approach -- Evolution and extinction under uncertainty -- Sustainable consumption and uncertainty -- Mathematical preliminaries.
Author | : V.V. Fedorov |
Publisher | : Elsevier |
Total Pages | : 307 |
Release | : 2013-04-20 |
Genre | : Technology & Engineering |
ISBN | : 0323162460 |
Theory Of Optimal Experiments