This book presents comprehensive state-of-the-art theoretical analysis of the fundamental Newtonian and Newtonian-related approaches to solving optimization and variational problems. A central focus is the relationship between the basic Newton scheme for a given problem and algorithms that also enjoy fast local convergence. The authors develop general perturbed Newtonian frameworks that preserve fast convergence and consider specific algorithms as particular cases within those frameworks, i.e., as perturbations of the associated basic Newton iterations. This approach yields a set of tools for...
This book presents comprehensive state-of-the-art theoretical analysis of the fundamental Newtonian and Newtonian-related approaches to solving optimi...
The implicit function theorem is one of the most important theorems in analysis and its many variants are basic tools in partial differential equations and numerical analysis.
This second edition of Implicit Functions and Solution Mappings presents an updated and more complete picture of the field by including solutions of problems that have been solved since the first edition was published, and places old and new results in a broader perspective. The purpose of this self-contained work is to provide a reference on the topic and to provide a unified collection of a number of...
The implicit function theorem is one of the most important theorems in analysis and its many variants are basic tools in partial differential equat...
A presentation of general results for discussing local optimality and computation of the expansion of value function and approximate solution of optimization problems, followed by their application to various fields, from physics to economics. The book is thus an opportunity for popularizing these techniques among researchers involved in other sciences, including users of optimization in a wide sense, in mechanics, physics, statistics, finance and economics. Of use to research professionals, including graduate students at an advanced level.
A presentation of general results for discussing local optimality and computation of the expansion of value function and approximate solution of optim...
The book contains description of a real life application of modern mathematical optimization tools in an important problem solution for power networks. 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. The physical parameters of the network are also taken into account. The obtained large-scale mixed variable problem is relaxed in a smart,...
The book contains description of a real life application of modern mathematical optimization tools in an important problem solution for power netwo...
Multistage stochastic optimization problems appear in many ways in finance, insurance, energy production and trading, logistics and transportation, among other areas. They describe decision situations under uncertainty and with a longer planning horizon. This book contains a comprehensive treatment of today's state of the art in multistage stochastic optimization. It covers the mathematical backgrounds of approximation theory as well as numerous practical algorithms and examples for the generation and handling of scenario trees. A special emphasis is put on estimation and bounding of the...
Multistage stochastic optimization problems appear in many ways in finance, insurance, energy production and trading, logistics and transportation, am...
Investment and risk management problems are fundamental problems for financial institutions and involve both speculative and hedging decisions. A structured approach to these problems naturally leads one to the field of applied mathematics in order to translate subjective probability beliefs and attitudes towards risk and reward into actual decisions.
In Risk and Portfolio Analysis the authors present sound principles and useful methods for making investment and risk management decisions in the presence of hedgeable and non-hedgeable risks using the simplest possible...
Investment and risk management problems are fundamental problems for financial institutions and involve both speculative and hedging decisions. A s...
The author's particular interest in the area of risk measures is to combine this theory with the analysis of dependence properties. The present volume gives an introduction of basic concepts and methods in mathematical risk analysis, in particular of those parts of risk theory that are of special relevance to finance and insurance. Describing the influence of dependence in multivariate stochastic models on risk vectors is the main focus of the text that presents main ideas and methods as well as their relevance to practical applications. The first part introduces basic probabilistic tools and...
The author's particular interest in the area of risk measures is to combine this theory with the analysis of dependence properties. The present volume...
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...
Heavy-tailed probability distributions are an important component in the modeling of many stochastic systems. They are frequently used to accuratel...
In this monograph the authors give a systematic approach to the probabilistic properties of the fixed point equation X=AX+B. A probabilistic study of the stochastic recurrence equation X_t=A_tX_{t-1}+B_t for real- and matrix-valued random variables A_t, where (A_t, B_t) constitute an iid sequence, is provided. The classical theory for these equations, including the existence and uniqueness of a stationary solution, the tail behavior with special emphasis on power law behavior, moments and support, is presented. The authors collect recent asymptotic results on extremes, point processes,...
In this monograph the authors give a systematic approach to the probabilistic properties of the fixed point equation X=AX+B. A probabilistic study ...
Applying the philosophy, theory, and methods of decision analysis to creating and executing winning legal strategies, this book offers explanations from introductory to advanced, with practice problems at the end of each chapter and numerous step-by-step tutorials as well as complete examples of how to structure most common legal questions.
Applying the philosophy, theory, and methods of decision analysis to creating and executing winning legal strategies, this book offers explanations fr...