Pareto Optimality, Game Theory and Equilibria

Pareto Optimality, Game Theory and Equilibria
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.

Robust Optimization

Robust Optimization
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.

Encyclopedia of Global Justice

Encyclopedia of Global Justice
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.

Adaptationism and Optimality

Adaptationism and Optimality
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.

Optimality Conditions: Abnormal and Degenerate Problems

Optimality Conditions: Abnormal and Degenerate Problems
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.

Fuzzy Sets and Interactive Multiobjective Optimization

Fuzzy Sets and Interactive Multiobjective Optimization
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.

Theory of Optimal Designs

Theory of Optimal Designs
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.

Optimal Design of Experiments

Optimal Design of Experiments
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.

Sustainability and Resources

Sustainability and Resources
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.

Theory Of Optimal Experiments

Theory Of Optimal Experiments
Author: V.V. Fedorov
Publisher: Elsevier
Total Pages: 307
Release: 2013-04-20
Genre: Technology & Engineering
ISBN: 0323162460

Theory Of Optimal Experiments