Theory Of Optimal Search

In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation; methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; and methods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory. As a result, the book represents a blend of new methods in general computational analysis, and specific, but also generic, techniques for study of systems theory ant its particular branches, such as optimal filtering and information compression. - Best operator approximation, - Non-Lagrange interpolation, - Generic Karhunen-Loeve transform - Generalised low-rank matrix approximation - Optimal data compression - Optimal nonlinear filtering

This book begins with a review of basic results in optimal search for a stationary target. It then develops the theory of optimal search for a moving target, providing algorithms for computing optimal plans and examples of their use. Next it develops methods for computing optimal search plans involving multiple targets and multiple searchers with realistic operational constraints on search movement. These results assume that the target does not react to the search. In the final chapter there is a brief overview of mostly military problems where the target tries to avoid being found as well as rescue or rendezvous problems where the target and the searcher cooperate. Larry Stone wrote his definitive book Theory of Optimal Search in 1975, dealing almost exclusively with the stationary target search problem. Since then the theory has advanced to encompass search for targets that move even as the search proceeds, and computers have developed sufficient capability to employ the improved theory. In this book, Stone joins Royset and Washburn to document and explain this expanded theory of search. The problem of how to search for moving targets arises every day in military, rescue, law enforcement, and border patrol operations.

On the solution of an optimal search problem with an exponential detection function. Covers one- and two-sided detection problems by furnishing continuous and discret time strategies; examines two-sided search strategies with solutions in hide and seek games in many discrete and continuous bounded

Search theory is concerned with the location of a 'target' given imprecise information concerning its location. The subject has a variety of applications such as locating missing people in wilderness or at sea, searching for mineral deposits, medical diagnosis, and searching for malfunctions in industrial processes. This volume is concerned with search strategies which are optimal in the sense that they minimize the 'risk' or cost of a search where this may be measured in factors such as time or money. Consequently, the author discusses a range of mathematical techniques including non-linear programming, fractional programming, dynamic programming, the calculus of variation, and the Pontryagin maximum principle from optimal control theory. Many numerical examples are presented in order to illustrate the effectiveness of particular techniques. As a result, this book will provide all researchers in search theory with an up-to-date account of this important area of operations research.

The NATO Advanced Research Institute on Search Theory and Appli cations was held at the Hotel Algarve in Praia Da Rocha, Portugal, from March 26 through March 30, 1979, and was sponsored by the NATO Special Programme Panel on Systems Science. There were forty-one participants representing a wide range of backgrounds and interests. The purpose of the institute was to bring together people working in search theory and applications with potential users of search techniques to stimulate the increased application of recent ly developed search technology to civilian problems such as search and rescue, mineral exploration, surveillance, and fishing. Con versely, it was felt that by exposing search analysts to potential applications and new problems, they would be stimulated to develop new techniques for these applications and problems. The exchange of ideas and problems necessary to accomplish these goals was provided in the meeting workshops. There were three workshops, Search and Rescue, Exploration, and Surveillance and Fishing, each consisting of a small group of search analysts and potential users working together to define areas in which search theory and technology can be applied and to outline plans for im plementation. At the end of the conference, each working group submitted a report outlining possible areas of search applications and discussing problems which needed to be solved in order to im plement these applications.

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.

In this monograph, the authors develop a methodology that allows one to construct and substantiate optimal and suboptimal algorithms to solve problems in computational and applied mathematics. Throughout the book, the authors explore well-known and proposed algorithms with a view toward analyzing their quality and the range of their efficiency. The concept of the approach taken is based on several theories (of computations, of optimal algorithms, of interpolation, interlination, and interflatation of functions, to name several). Theoretical principles and practical aspects of testing the quality of algorithms and applied software, are a major component of the exposition. The computer technology in construction of T-efficient algorithms for computing ε-solutions to problems of computational and applied mathematics, is also explored. The readership for this monograph is aimed at scientists, postgraduate students, advanced students, and specialists dealing with issues of developing algorithmic and software support for the solution of problems of computational and applied mathematics.