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Empirical Estimates in Stochastic Optimization and Identification
This book contains problems of stochastic optimization and identification. Results concerning uniform law of large numbers, convergence of approximate estimates of extreme points, as well as empirical estimates of functionals with probability 1 and in probability are presented. Audience: Specialists in stochastic optimization and estimations, postgraduate students, and graduate students studying such topics
Estimation and Control Problems for Stochastic Partial Differential Equations
Focusing on research surrounding aspects of insufficiently studied problems of estimation and optimal control of random fields, this book exposes some important aspects of those fields for systems modeled by stochastic partial differential equations. It contains many results of interest to specialists in both the theory of random fields and optimal control theory who use modern mathematical tools for resolving specific applied problems, and presents research that has not previously been covered. More generally, this book is intended for scientists, graduate, and post-graduates specializing in probability theory and mathematical statistics. The models presented describe many processes in turb...
Modern Optimization Methods for Decision Making Under Risk and Uncertainty
The book comprises original articles on topical issues of risk theory, rational decision making, statistical decisions, and control of stochastic systems. The articles are the outcome of a series international projects involving the leading scholars in the field of modern stochastic optimization and decision making. The structure of stochastic optimization solvers is described. The solvers in general implement stochastic quasi-gradient methods for optimization and identification of complex nonlinear models. These models constitute an important methodology for finding optimal decisions under risk and uncertainty. While a large part of current approaches towards optimization under uncertainty ...
Regression Analysis Under A Priori Parameter Restrictions
This monograph focuses on the construction of regression models with linear and non-linear constrain inequalities from the theoretical point of view. Unlike previous publications, this volume analyses the properties of regression with inequality constrains, investigating the flexibility of inequality constrains and their ability to adapt in the presence of additional a priori information The implementation of inequality constrains improves the accuracy of models, and decreases the likelihood of errors. Based on the obtained theoretical results, a computational technique for estimation and prognostication problems is suggested. This approach lends itself to numerous applications in various practical problems, several of which are discussed in detail The book is useful resource for graduate students, PhD students, as well as for researchers who specialize in applied statistics and optimization. This book may also be useful to specialists in other branches of applied mathematics, technology, econometrics and finance
Control of Spatially Structured Random Processes and Random Fields with Applications
This book is devoted to the study and optimization of spatiotemporal stochastic processes - processes which develop simultaneously in space and time under random influences. These processes are seen to occur almost everywhere when studying the global behavior of complex systems. The book presents problems and content not considered in other books on controlled Markov processes, especially regarding controlled Markov fields on graphs.
Probabilistic Constrained Optimization
Probabilistic and percentile/quantile functions play an important role in several applications, such as finance (Value-at-Risk), nuclear safety, and the environment. Recently, significant advances have been made in sensitivity analysis and optimization of probabilistic functions, which is the basis for construction of new efficient approaches. This book presents the state of the art in the theory of optimization of probabilistic functions and several engineering and finance applications, including material flow systems, production planning, Value-at-Risk, asset and liability management, and optimal trading strategies for financial derivatives (options). Audience: The book is a valuable source of information for faculty, students, researchers, and practitioners in financial engineering, operation research, optimization, computer science, and related areas.
Optimization and Related Topics
This volume contains, in part, a selection of papers presented at the sixth Australian Optimization Day Miniconference (Ballarat, 16 July 1999), and the Special Sessions on Nonlinear Dynamics and Optimization and Operations Re search - Methods and Applications, which were held in Melbourne, July 11-15 1999 as a part of the Joint Meeting of the American Mathematical Society and Australian Mathematical Society. The editors have strived to present both con tributed papers and survey style papers as a more interesting mix for readers. Some participants from the meetings mentioned above have responded to this approach by preparing survey and 'semi-survey' papers, based on presented lectures. Cont...
Optimization Methods and Applications
Researchers and practitioners in computer science, optimization, operations research and mathematics will find this book useful as it illustrates optimization models and solution methods in discrete, non-differentiable, stochastic, and nonlinear optimization. Contributions from experts in optimization are showcased in this book showcase a broad range of applications and topics detailed in this volume, including pattern and image recognition, computer vision, robust network design, and process control in nonlinear distributed systems. This book is dedicated to the 80th birthday of Ivan V. Sergienko, who is a member of the National Academy of Sciences (NAS) of Ukraine and the director of the V.M. Glushkov Institute of Cybernetics. His work has had a significant impact on several theoretical and applied aspects of discrete optimization, computational mathematics, systems analysis and mathematical modeling.
Simulation and Optimization Methods in Risk and Reliability Theory
This book introduces recent advances in the area of risk estimation in complex systems. The authors study new methods of accelerated modelling, asymptotical analysis and optimal estimating. The processes are modelled using large failure trees, the methodology of fuzzy sets, bayesians, methods of stochastic optimisation, and optimal models of equipment service and control. The authors suggest applying numerical methods for analysis of super-large failure trees having large amount of multiple vertices. The methods allow finding minimal sections and reducing the amount of time necessary for such calculations. The Bayesians theory is applied under conditions of uncertainty. The methods of finding robust parameter estimates for the most commonly used classes of a priori distribution functions are suggested. As an alternative approach to stochastic methods the authors propose the algorithums of critical stats estimation for the reactor's active zone that utilise the theory of fuzzy logic.
Mathematical Reviews
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