Minimax Models In The Theory Of Numerical Methods
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Minimax Models In The Theory Of Numerical Methods
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Author : A. Sukharev
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Minimax Models In The Theory Of Numerical Methods written by A. Sukharev and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Business & Economics categories.
In the Russian edition published in 1989, this book was called "Minimax Algorithms in Problems of Numerical Analysis". The new title is better related to the subject of the book and its style. The basis for every decision or inference concerning the ways to solve a given problem is the computa tion model. Thus, the computation model is the epicenter of any structure studied in the book. Algorithms are not constructed here, they are rather derived from computation models. Quality of an algorithm depends entirely on consistency of the model with the real-life problem. So, constructing a model is an art, deriving an algorithm is a science. We study only minimax or, in other words, worst-case computation models. However, one of the characteristic features of the book is a new approach to the notion of the worst-case conditions in dynamic processes. This approach leads to the concept of sequentially optimal algorithms, which play the central role in the book. In conclusion, I would like to express my gratitude to Prof. Dr. Heinz J. Skala and Dr. Sergei A. Orlovsky for encouraging translation of this book. I also greatly appreciate the highly professional job of Dr. Olga R. Chuyan who translated the book.
Arrovian Aggregation Models
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Author : Fuad T. Aleskerov
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Arrovian Aggregation Models written by Fuad T. Aleskerov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Business & Economics categories.
Aggregation of individual opinions into a social decision is a problem widely observed in everyday life. For centuries people tried to invent the `best' aggregation rule. In 1951 young American scientist and future Nobel Prize winner Kenneth Arrow formulated the problem in an axiomatic way, i.e., he specified a set of axioms which every reasonable aggregation rule has to satisfy, and obtained that these axioms are inconsistent. This result, often called Arrow's Paradox or General Impossibility Theorem, had become a cornerstone of social choice theory. The main condition used by Arrow was his famous Independence of Irrelevant Alternatives. This very condition pre-defines the `local' treatment of the alternatives (or pairs of alternatives, or sets of alternatives, etc.) in aggregation procedures. Remaining within the framework of the axiomatic approach and based on the consideration of local rules, Arrovian Aggregation Models investigates three formulations of the aggregation problem according to the form in which the individual opinions about the alternatives are defined, as well as to the form of desired social decision. In other words, we study three aggregation models. What is common between them is that in all models some analogue of the Independence of Irrelevant Alternatives condition is used, which is why we call these models Arrovian aggregation models. Chapter 1 presents a general description of the problem of axiomatic synthesis of local rules, and introduces problem formulations for various versions of formalization of individual opinions and collective decision. Chapter 2 formalizes precisely the notion of `rationality' of individual opinions and social decision. Chapter 3 deals with the aggregation model for the case of individual opinions and social decisions formalized as binary relations. Chapter 4 deals with Functional Aggregation Rules which transform into a social choice function individual opinions defined as choice functions. Chapter 5 considers another model – Social Choice Correspondences when the individual opinions are formalized as binary relations, and the collective decision is looked for as a choice function. Several new classes of rules are introduced and analyzed.
A Course In Mathematical And Statistical Ecology
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Author : Anil Gore
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
A Course In Mathematical And Statistical Ecology written by Anil Gore and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.
As the world enters the new millennium, mankind faces a series ofnew prob lems, many of them created by man himself. These include overpopulation, air and water pollution, global warming, accumulation of greenhouse gases, darnage to the ozone layer and loss of biodiversity. Perhaps these problems were around even earlier in an incipient stage, but they have now assumed global proportions and are uppermost in the minds of all. A natural con sequence is enhanced interest in sciences connected with these problems. Ecology is a field that is immensely useful in understanding many of them. In the seventies, nature conservation became a concern of wide sections of society, well beyond the small group of expert ecologists. Species extinc tion and depletion of biological resources were seen as major threats to human welfare. It was therefore natural for scientists from different disci plines to seek reasons behind these developments. We were no exceptions and when opportunity to interact with ecologists as statistreal consultants came, we found ourselves reading more and more of ecology and evolution ary biology. Several years ago we proposed starting of an elective one semester course on statistical ecology for graduate students of statistics of Pune University.
Models And Experiments In Risk And Rationality
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Author : Bertrand Munier
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Models And Experiments In Risk And Rationality written by Bertrand Munier and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Business & Economics categories.
Models and Experiments in Risk and Rationality presents original contributions to the areas of individual choice, experimental economics, operations and analysis, multiple criteria decision making, market uncertainty, game theory and social choice. The papers, which were presented at the FUR VI conference, are arranged to appear in order of increasing complexity of the decision environment or social context in which they situate themselves. The first section `Psychological Aspects of Risk-Bearing', considers choice at the purely individual level and for the most part, free of any specific economic or social context. The second section examines individual choice within the classical expected utility approach while the third section works from a perspective that includes non-expected utility preferences over lotteries. Section four, `Multiple Criteria Decision-Making Under Uncertainty', considers the more specialized but crucial context of uncertain choice involving tradeoffs between competing criteria -- a field which is becoming of increasing importance in applied decision analysis. The final two sections examine uncertain choice in social or group contexts.
Fundamentals Of Convex Analysis
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Author : M.J. Panik
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Fundamentals Of Convex Analysis written by M.J. Panik and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
Fundamentals of Convex Analysis offers an in-depth look at some of the fundamental themes covered within an area of mathematical analysis called convex analysis. In particular, it explores the topics of duality, separation, representation, and resolution. The work is intended for students of economics, management science, engineering, and mathematics who need exposure to the mathematical foundations of matrix games, optimization, and general equilibrium analysis. It is written at the advanced undergraduate to beginning graduate level and the only formal preparation required is some familiarity with set operations and with linear algebra and matrix theory. Fundamentals of Convex Analysis is self-contained in that a brief review of the essentials of these tool areas is provided in Chapter 1. Chapter exercises are also provided. Topics covered include: convex sets and their properties; separation and support theorems; theorems of the alternative; convex cones; dual homogeneous systems; basic solutions and complementary slackness; extreme points and directions; resolution and representation of polyhedra; simplicial topology; and fixed point theorems, among others. A strength of this work is how these topics are developed in a fully integrated fashion.
Statistical Analysis Of Observations Of Increasing Dimension
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Author : V.L. Girko
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Statistical Analysis Of Observations Of Increasing Dimension written by V.L. Girko and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
Statistical Analysis of Observations of Increasing Dimension is devoted to the investigation of the limit distribution of the empirical generalized variance, covariance matrices, their eigenvalues and solutions of the system of linear algebraic equations with random coefficients, which are an important function of observations in multidimensional statistical analysis. A general statistical analysis is developed in which observed random vectors may not have density and their components have an arbitrary dependence structure. The methods of this theory have very important advantages in comparison with existing methods of statistical processing. The results have applications in nuclear and statistical physics, multivariate statistical analysis in the theory of the stability of solutions of stochastic differential equations, in control theory of linear stochastic systems, in linear stochastic programming, in the theory of experiment planning.
Limit Theorems And Applications Of Set Valued And Fuzzy Set Valued Random Variables
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Author : Shoumei Li
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Limit Theorems And Applications Of Set Valued And Fuzzy Set Valued Random Variables written by Shoumei Li and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.
After the pioneering works by Robbins {1944, 1945) and Choquet (1955), the notation of a set-valued random variable (called a random closed set in literatures) was systematically introduced by Kendall {1974) and Matheron {1975). It is well known that the theory of set-valued random variables is a natural extension of that of general real-valued random variables or random vectors. However, owing to the topological structure of the space of closed sets and special features of set-theoretic operations ( cf. Beer [27]), set-valued random variables have many special properties. This gives new meanings for the classical probability theory. As a result of the development in this area in the past more than 30 years, the theory of set-valued random variables with many applications has become one of new and active branches in probability theory. In practice also, we are often faced with random experiments whose outcomes are not numbers but are expressed in inexact linguistic terms.
Bayesian And High Dimensional Global Optimization
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Author : Anatoly Zhigljavsky
language : en
Publisher: Springer Nature
Release Date : 2021-03-02
Bayesian And High Dimensional Global Optimization written by Anatoly Zhigljavsky and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-02 with Mathematics categories.
Accessible to a variety of readers, this book is of interest to specialists, graduate students and researchers in mathematics, optimization, computer science, operations research, management science, engineering and other applied areas interested in solving optimization problems. Basic principles, potential and boundaries of applicability of stochastic global optimization techniques are examined in this book. A variety of issues that face specialists in global optimization are explored, such as multidimensional spaces which are frequently ignored by researchers. The importance of precise interpretation of the mathematical results in assessments of optimization methods is demonstrated through examples of convergence in probability of random search. Methodological issues concerning construction and applicability of stochastic global optimization methods are discussed, including the one-step optimal average improvement method based on a statistical model of the objective function. A significant portion of this book is devoted to an analysis of high-dimensional global optimization problems and the so-called ‘curse of dimensionality’. An examination of the three different classes of high-dimensional optimization problems, the geometry of high-dimensional balls and cubes, very slow convergence of global random search algorithms in large-dimensional problems , and poor uniformity of the uniformly distributed sequences of points are included in this book.
Mathematics Of Data Fusion
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Author : I.R. Goodman
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Mathematics Of Data Fusion written by I.R. Goodman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.
Data fusion or information fusion are names which have been primarily assigned to military-oriented problems. In military applications, typical data fusion problems are: multisensor, multitarget detection, object identification, tracking, threat assessment, mission assessment and mission planning, among many others. However, it is clear that the basic underlying concepts underlying such fusion procedures can often be used in nonmilitary applications as well. The purpose of this book is twofold: First, to point out present gaps in the way data fusion problems are conceptually treated. Second, to address this issue by exhibiting mathematical tools which treat combination of evidence in the presence of uncertainty in a more systematic and comprehensive way. These techniques are based essentially on two novel ideas relating to probability theory: the newly developed fields of random set theory and conditional and relational event algebra. This volume is intended to be both an update on research progress on data fusion and an introduction to potentially powerful new techniques: fuzzy logic, random set theory, and conditional and relational event algebra. Audience: This volume can be used as a reference book for researchers and practitioners in data fusion or expert systems theory, or for graduate students as text for a research seminar or graduate level course.
Fundamentals Of Uncertainty Calculi With Applications To Fuzzy Inference
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Author : Michel Grabisch
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Fundamentals Of Uncertainty Calculi With Applications To Fuzzy Inference written by Michel Grabisch and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Business & Economics categories.
With the vision that machines can be rendered smarter, we have witnessed for more than a decade tremendous engineering efforts to implement intelligent sys tems. These attempts involve emulating human reasoning, and researchers have tried to model such reasoning from various points of view. But we know precious little about human reasoning processes, learning mechanisms and the like, and in particular about reasoning with limited, imprecise knowledge. In a sense, intelligent systems are machines which use the most general form of human knowledge together with human reasoning capability to reach decisions. Thus the general problem of reasoning with knowledge is the core of design methodology. The attempt to use human knowledge in its most natural sense, that is, through linguistic descriptions, is novel and controversial. The novelty lies in the recognition of a new type of un certainty, namely fuzziness in natural language, and the controversality lies in the mathematical modeling process. As R. Bellman [7] once said, decision making under uncertainty is one of the attributes of human intelligence. When uncertainty is understood as the impossi bility to predict occurrences of events, the context is familiar to statisticians. As such, efforts to use probability theory as an essential tool for building intelligent systems have been pursued (Pearl [203], Neapolitan [182)). The methodology seems alright if the uncertain knowledge in a given problem can be modeled as probability measures.