This textbook highlights the many practical uses of stable distributions, exploring the theory, numerical algorithms, and statistical methods used to work with stable laws. Because of the author’s accessible and comprehensive approach, readers will be able to understand and use these methods. Both mathematicians and non-mathematicians will find this a valuable resource for more accurately modelling and predicting large values in a number of real-world scenarios.
Beginning with an introductory chapter that explains key ideas about stable laws, readers will be...
This textbook highlights the many practical uses of stable distributions, exploring the theory, numerical algorithms, and statistical methods use...
This book presents a unified theory of convex functions, sets, and set-valued mappings in topological vector spaces with its specifications to locally convex, Banach and finite-dimensional settings. These developments and expositions are based on the powerful geometric approach of variational analysis, which resides on set extremality with its characterizations and specifications in the presence of convexity. Using this approach, the text consolidates the device of fundamental facts of generalized differential calculus to obtain novel results for convex sets, functions, and set-valued...
This book presents a unified theory of convex functions, sets, and set-valued mappings in topological vector spaces with its specifications to lo...
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...
This monograph presents a comprehensive treatment of the maximum-entropy sampling problem (MESP), which is a fascinating topic at the intersection of ...
This book aims at an innovative approach within the framework of convex analysis and optimization, based on an in-depth study of the behavior and properties of the supremum of families of convex functions. It presents an original and systematic treatment of convex analysis, covering standard results and improved calculus rules in subdifferential analysis. The tools supplied in the text allow a direct approach to the mathematical foundations of convex optimization, in particular to optimality and duality theory. Other applications in the book concern convexification processes in...
This book aims at an innovative approach within the framework of convex analysis and optimization, based on an in-depth study of the behavior and prop...
This book explores regime-switching Brownian motion, a class of stochastic processes widely used in fields such as mathematical finance, risk theory, queueing theory, and epidemiological modeling. These processes are studied within the Markovian regime-switching framework, which captures dynamic environments characterized by shifts between different states or "regimes" for example, economic cycles, seasonal environmental variations, or short-term surges in activity.
The matrix-analytic approach, introduced approximately fifty years ago in the context of classical queueing theory,...
This book explores regime-switching Brownian motion, a class of stochastic processes widely used in fields such as mathematical finance, risk theor...
This fundamental work is a sequel to monographs by the same author: Variational Analysis and Applications (2018) and the two Grundlehren volumes Variational Analysis and Generalized Differentiation: I Basic Theory, II Applications (2006). This present book is the first entirely devoted to second-order variational analysis with numerical algorithms and applications to practical models. It covers a wide range of topics including theoretical, numerical, and implementations that will interest researchers in analysis, applied mathematics, mathematical economics,...
This fundamental work is a sequel to monographs by the same author: Variational Analysis and Applications (2018) and the two Grundleh...
This is an updated version of what is still the only text to address basic questions about how to model uncertainty in mathematical programming, including how to reformulate a deterministic model so that it can be analyzed in a stochastic setting. This second edition has important extensions regarding how to represent random phenomena in the models (also called scenario generation) as well as a new chapter on multi-stage models.
This text would be suitable as a stand-alone or supplement for a second course in OR/MS or in optimization-oriented engineering...
This is an updated version of what is still the only text to address basic questions about how to model uncertainty in mathematical pro...
This book offers a comprehensive presentation of the theory and methods of risk-averse optimization and control. Problems of this type arise in finance, energy production and distribution, supply chain management, medicine, and many other areas, where not only the average performance of a stochastic system is essential, but also high-impact and low-probability events must be taken into account. The book is a self-contained presentation of the utility theory, the theory of measures of risk, including systemic and dynamic measures of risk, and their use in optimization and control models. It...
This book offers a comprehensive presentation of the theory and methods of risk-averse optimization and control. Problems of this type arise in fin...
