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This monograph presents a comprehensive treatment of the maximum-entropy sampling problem (MESP), which is a fascinating topic at the intersection of mathematical optimization and data science. The text situates MESP in information theory, as the algorithmic problem of calculating a sub-vector of pre-specificed size from a multivariate Gaussian random vector, so as to maximize Shannon's differential entropy. The text collects and expands on state-of-the-art algorithms for MESP, and addresses its application in the field of environmental monitoring. While MESP is a central optimization problem in the theory of statistical designs (particularly in the area of spatial monitoring), this book largely focuses on the unique challenges of its algorithmic side. From the perspective of mathematical-optimization methodology, MESP is rather unique (a 0/1 nonlinear program having a nonseparable objective function), and the algorithmic techniques employed are highly non-standard. In particular, successful techniques come from several disparate areas within the field of mathematical optimization; for example: convex optimization and duality, semidefinite programming, Lagrangian relaxation, dynamic programming, approximation algorithms, 0/1 optimization (e.g., branch-and-bound), extended formulation, and many aspects of matrix theory. The book is mainly aimed at graduate students and researchers in mathematical optimization and data analytics. 

This richly illustrated book introduces the subject of optimization to a broad audience with a balanced treatment of theory, models and algorithms. Through numerous examples from statistical learning, operations research, engineering, finance and economics, the text explains how to formulate and justify models while accounting for real-world considerations such as data uncertainty. It goes beyond the classical topics of linear, nonlinear and convex programming and deals with nonconvex and nonsmooth problems as well as games, generalized equations and stochastic optimization.The book teaches theoretical aspects in the context of concrete problems, which makes it an accessible onramp to variational analysis, integral functions and approximation theory. More than 100 exercises and 200 fully developed examples illustrate the application of the concepts. Readers should have some foundation in differential calculus and linear algebra. Exposure to real analysiswould be helpful but is not prerequisite.

This treatment of extreme value theory is unique in book literature in that it focuses on some beautiful theoretical results along with applications. All the main topics covering the heart of the subject are introduced to the reader in a systematic fashion so that in the final chapter even the most recent developments in the theory can be understood.Key to the presentation is the concentration on the probabilistic and statistical aspects of extreme values without major emphasis on such related topics as regular variation, point processes, empirical distribution functions, and Brownian motion.The work is an excellent introduction to extreme value theory at the graduate level, requiring only some mathematical maturity.

Heavy-tailed probability distributions are an important component in the modeling of many stochastic systems. They are frequently used to accurately model inputs and outputs of computer and data networks and service facilities such as call centers. They are an essential for describing risk processes in finance and also for insurance premia pricing, and such distributions occur naturally in models of epidemiological spread. The class includes distributions with power law tails such as the Pareto, as well as the lognormal and certain Weibull distributions.One of the highlights of this new edition is that it includes problems at the end of each chapter. Chapter 5 is also updated to include interesting applications to queueing theory, risk, and branching processes. New results are presented in a simple, coherent and systematic way.Graduate students as well as modelers in the fields of finance, insurance, network science and environmental studies will find this book to be an essential reference.

The main subject of this book is perturbation analysis of continuous optimization problems. In the last two decades considerable progress has been made in that area, and it seems that it is time now to present a synthetic view of many important results that apply to various classes of problems. The model problem that is considered throughout the book is of the form (P) Min/(x) subjectto G(x) E K. xeX Here X and Y are Banach spaces, K is a closed convex subset of Y, and / : X -+ IR and G : X -+ Y are called the objective function and the constraint mapping, respectively. We also consider a parameteriZed version (P ) of the above u problem, where the objective function / (x, u) and the constraint mapping G(x, u) are parameterized by a vector u varying in a Banach space U. Our aim is to study continuity and differentiability properties of the optimal value v(u) and the set S(u) of optimal solutions of (P ) viewed as functions of the parameter vector u.

This textbook highlights the many practical uses of stable distributions, exploring the theory, numerical algorithms, and statistical methods used to work with stable laws.

This richly illustrated book introduces the subject of optimization to a broad audience with a balanced treatment of theory, models and algorithms. Through numerous examples from statistical learning, operations research, engineering, finance and economics, the text explains how to formulate and justify models while accounting for real-world considerations such as data uncertainty. It goes beyond the classical topics of linear, nonlinear and convex programming and deals with nonconvex and nonsmooth problems as well as games, generalized equations and stochastic optimization.The book teaches theoretical aspects in the context of concrete problems, which makes it an accessible onramp to variational analysis, integral functions and approximation theory. More than 100 exercises and 200 fully developed examples illustrate the application of the concepts. Readers should have some foundation in differential calculus and linear algebra. Exposure to real analysiswould be helpful but is not prerequisite.

This book aims to present a comprehensive, self-contained, and concise overview of extreme value theory for time series, incorporating the latest research trends alongside classical methodology.

There has been an increase in attention toward systems involving large numbers of small players, giving rise to the theory of mean field games, mean field type control and nonlinear Markov games.

Part III presents direct search methods (Generalized Pattern Search and Mesh Adaptive Direct Search) and Part IV focuses on model-based methods (Simplex Gradient and Trust Region).

This monograph is a gateway for researchers and graduate students to explore the profound, yet subtle, world of long-range dependence (also known as long memory).

This book presents state-of-the-art theoretical analysis of fundamental Newtonian and Newtonian-related approaches to solving optimization and variational problems, and offers a set of tools for the unified treatment of various algorithms.

This book is the first in-depth guide to applying the philosophy, theory, and methods of decision analysis to creating and executing winning legal strategies.

This book reviews basic terminology, concepts, taxonomy and tenets of inventory systems, then explores models: EOQ, lot-sizing, Newsvendor, continuous time and more. The authors discuss in detail different real situations in industry and theoretical models.

Multistage stochastic optimization problems appear in many ways in finance, insurance, energy production and trading, logistics and transportation, among other areas.

The objective is the modelling and calculation of optimal daily scheduling of power generation, by thermal power plants, to satisfy all demands at minimum cost, in such a way that the generation and transmission capacities as well as the demands at the nodes of the system appear in an integrated form.

Implicit Functions and Solution Mappings

This book, written for the logistics manager and researcher, presents an authoritative survey of the modern theory and application of logistics, including case studies in which decision support tools for large-scale logistics applications are developed.

"This is an excellent and well-written text on discrete event simulation with a focus on applications in Operations Research. Methods are provided for generating pseudo-random numbers (including combining such streams) and for generating random numbers from most standard statistical distributions."

This text gives an interesting and useful blend of the mathematical, probabilistic and statistical tools used in heavy-tail analysis. It is uniquely devoted to heavy-tails and emphasizes both probability modeling and statistical methods for fitting models.

Apart from a thorough exploration of all the important concepts, this volume includes over 75 algorithms, ready for putting into practice. Readers are assumed to have a sound understanding of calculus, introductory matrix analysis, and intermediate statistics, but otherwise the book is self-contained.

The up-to-date material and logical structure of this volume provides the clarity and orientation needed to gain a solid working knowledge of mathematical risk analysis. It includes a specialized focus on the risk theory deployed in finance and insurance.

This new edition offers updated content and an outlook on further results, extensions and generalizations on stopped random walks. It also contains a new chapter on perturbed random walks and nearly 100 new bibliographic references.

This book analyzes and compares four closely related problems, namely linear programming, integer programming, linear integration, and linear summation (or counting). The book provides some new insights on duality concepts for integer programs.

In an extensively updated new edition, this book teaches stochastic programming, with new approaches for discrete variables, new results on risk measures in modeling and Monte Carlo sampling methods, a new chapter on relationships to other methods and more.

Looks at quality management in a new way; Offers a very different mathematical tool set than traditionally employed for quality control problems; Yao is a leading researcher in the area of stochastic modeling and the author of a previous Springer book