Risk-Averse Optimization and Control
Author : Darinka Dentcheva
Publisher : Springer Nature
Page : 462 pages
File Size : 12,7 MB
Release :
Category :
ISBN : 3031579887
Lectures on Stochastic Programming
Author : Alexander Shapiro
Publisher : SIAM
Page : 447 pages
File Size : 23,59 MB
Release : 2009-01-01
Category : Mathematics
ISBN : 0898718759
Book Description
Optimization problems involving stochastic models occur in almost all areas of science and engineering, such as telecommunications, medicine, and finance. Their existence compels a need for rigorous ways of formulating, analyzing, and solving such problems. This book focuses on optimization problems involving uncertain parameters and covers the theoretical foundations and recent advances in areas where stochastic models are available. Readers will find coverage of the basic concepts of modeling these problems, including recourse actions and the nonanticipativity principle. The book also includes the theory of two-stage and multistage stochastic programming problems; the current state of the theory on chance (probabilistic) constraints, including the structure of the problems, optimality theory, and duality; and statistical inference in and risk-averse approaches to stochastic programming.
Optimal Control of PDEs under Uncertainty
Author : Jesús Martínez-Frutos
Publisher : Springer
Page : 138 pages
File Size : 25,19 MB
Release : 2018-08-30
Category : Mathematics
ISBN : 3319982109
Book Description
This book provides a direct and comprehensive introduction to theoretical and numerical concepts in the emerging field of optimal control of partial differential equations (PDEs) under uncertainty. The main objective of the book is to offer graduate students and researchers a smooth transition from optimal control of deterministic PDEs to optimal control of random PDEs. Coverage includes uncertainty modelling in control problems, variational formulation of PDEs with random inputs, robust and risk-averse formulations of optimal control problems, existence theory and numerical resolution methods. The exposition focusses on the entire path, starting from uncertainty modelling and ending in the practical implementation of numerical schemes for the numerical approximation of the considered problems. To this end, a selected number of illustrative examples are analysed in detail throughout the book. Computer codes, written in MatLab, are provided for all these examples. This book is adressed to graduate students and researches in Engineering, Physics and Mathematics who are interested in optimal control and optimal design for random partial differential equations.
Multistage Stochastic Optimization
Author : Georg Ch. Pflug
Publisher : Springer
Page : 309 pages
File Size : 42,48 MB
Release : 2014-11-12
Category : Business & Economics
ISBN : 3319088432
Book Description
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 modeling error using novel distance concepts, on time consistency and the role of model ambiguity in the decision process. An extensive treatment of examples from electricity production, asset liability management and inventory control concludes the book.
Linear-Quadratic Controls in Risk-Averse Decision Making
Author : Khanh D. Pham
Publisher : Springer Science & Business Media
Page : 157 pages
File Size : 18,93 MB
Release : 2012-10-23
Category : Mathematics
ISBN : 1461450799
Book Description
Linear-Quadratic Controls in Risk-Averse Decision Making cuts across control engineering (control feedback and decision optimization) and statistics (post-design performance analysis) with a common theme: reliability increase seen from the responsive angle of incorporating and engineering multi-level performance robustness beyond the long-run average performance into control feedback design and decision making and complex dynamic systems from the start. This monograph provides a complete description of statistical optimal control (also known as cost-cumulant control) theory. In control problems and topics, emphasis is primarily placed on major developments attained and explicit connections between mathematical statistics of performance appraisals and decision and control optimization. Chapter summaries shed light on the relevance of developed results, which makes this monograph suitable for graduate-level lectures in applied mathematics and electrical engineering with systems-theoretic concentration, elective study or a reference for interested readers, researchers, and graduate students who are interested in theoretical constructs and design principles for stochastic controlled systems.
Risk-Averse Capacity Control in Revenue Management
Author : Christiane Barz
Publisher : Springer Science & Business Media
Page : 167 pages
File Size : 24,46 MB
Release : 2007-08-02
Category : Business & Economics
ISBN : 3540730133
Book Description
This book revises the well-known capacity control problem in revenue management from the perspective of a risk-averse decision-maker. Modelling an expected utility maximizing decision maker, the problem is formulated as a risk-sensitive Markov decision process. Special emphasis is put on the existence of structured optimal policies. Numerical examples illustrate the results.
Dynamic Programming and Optimal Control
Author : Dimitri P. Bertsekas
Publisher :
Page : 543 pages
File Size : 21,91 MB
Release : 2005
Category : Mathematics
ISBN : 9781886529267
Book Description
"The leading and most up-to-date textbook on the far-ranging algorithmic methododogy of Dynamic Programming, which can be used for optimal control, Markovian decision problems, planning and sequential decision making under uncertainty, and discrete/combinatorial optimization. The treatment focuses on basic unifying themes, and conceptual foundations. It illustrates the versatility, power, and generality of the method with many examples and applications from engineering, operations research, and other fields. It also addresses extensively the practical application of the methodology, possibly through the use of approximations, and provides an extensive treatment of the far-reaching methodology of Neuro-Dynamic Programming/Reinforcement Learning. The first volume is oriented towards modeling, conceptualization, and finite-horizon problems, but also includes a substantive introduction to infinite horizon problems that is suitable for classroom use. The second volume is oriented towards mathematical analysis and computation, treats infinite horizon problems extensively, and provides an up-to-date account of approximate large-scale dynamic programming and reinforcement learning. The text contains many illustrations, worked-out examples, and exercises."--Publisher's website.
Nonlinear Optimization
Author : Andrzej Ruszczynski
Publisher : Princeton University Press
Page : 463 pages
File Size : 19,92 MB
Release : 2011-09-19
Category : Mathematics
ISBN : 1400841054
Book Description
Optimization is one of the most important areas of modern applied mathematics, with applications in fields from engineering and economics to finance, statistics, management science, and medicine. While many books have addressed its various aspects, Nonlinear Optimization is the first comprehensive treatment that will allow graduate students and researchers to understand its modern ideas, principles, and methods within a reasonable time, but without sacrificing mathematical precision. Andrzej Ruszczynski, a leading expert in the optimization of nonlinear stochastic systems, integrates the theory and the methods of nonlinear optimization in a unified, clear, and mathematically rigorous fashion, with detailed and easy-to-follow proofs illustrated by numerous examples and figures. The book covers convex analysis, the theory of optimality conditions, duality theory, and numerical methods for solving unconstrained and constrained optimization problems. It addresses not only classical material but also modern topics such as optimality conditions and numerical methods for problems involving nondifferentiable functions, semidefinite programming, metric regularity and stability theory of set-constrained systems, and sensitivity analysis of optimization problems. Based on a decade's worth of notes the author compiled in successfully teaching the subject, this book will help readers to understand the mathematical foundations of the modern theory and methods of nonlinear optimization and to analyze new problems, develop optimality theory for them, and choose or construct numerical solution methods. It is a must for anyone seriously interested in optimization.
Solving Urban Infrastructure Problems Using Smart City Technologies
Author : John R. Vacca
Publisher : Elsevier
Page : 820 pages
File Size : 45,31 MB
Release : 2020-09-22
Category : Political Science
ISBN : 012816817X
Book Description
Solving Urban Infrastructure Problems Using Smart City Technologies is the most complete guide for integrating next generation smart city technologies into the very foundation of urban areas worldwide, showing how to make urban areas more efficient, more sustainable, and safer. Smart cities are complex systems of systems that encompass all aspects of modern urban life. A key component of their success is creating an ecosystem of smart infrastructures that can work together to enable dynamic, real-time interactions between urban subsystems such as transportation, energy, healthcare, housing, food, entertainment, work, social interactions, and governance. Solving Urban Infrastructure Problems Using Smart City Technologies is a complete reference for building a holistic, system-level perspective on smart and sustainable cities, leveraging big data analytics and strategies for planning, zoning, and public policy. It offers in-depth coverage and practical solutions for how smart cities can utilize resident's intellectual and social capital, press environmental sustainability, increase personalization, mobility, and higher quality of life. - Brings together experts from academia, government and industry to offer state-of- the-art solutions for urban system problems, showing how smart technologies can be used to improve the lives of the billions of people living in cities across the globe - Demonstrates practical implementation solutions through real-life case studies - Enhances reader comprehension with learning aid such as hands-on exercises, questions and answers, checklists, chapter summaries, chapter review questions, exercise problems, and more
Resilient Controls for Ordering Uncertain Prospects
Author : Khanh D. Pham
Publisher : Springer
Page : 222 pages
File Size : 34,5 MB
Release : 2014-09-05
Category : Mathematics
ISBN : 3319087053
Book Description
Providing readers with a detailed examination of resilient controls in risk-averse decision, this monograph is aimed toward researchers and graduate students in applied mathematics and electrical engineering with a systems-theoretic concentration. This work contains a timely and responsive evaluation of reforms on the use of asymmetry or skewness pertaining to the restrictive family of quadratic costs that have been appeared in various scholarly forums. Additionally, the book includes a discussion of the current and ongoing efforts in the usage of risk, dynamic game decision optimization and disturbance mitigation techniques with output feedback measurements tailored toward the worst-case scenarios. This work encompasses some of the current changes across uncertainty quantification, stochastic control communities, and the creative efforts that are being made to increase the understanding of resilient controls. Specific considerations are made in this book for the application of decision theory to resilient controls of the linear-quadratic class of stochastic dynamical systems. Each of these topics are examined explicitly in several chapters. This monograph also puts forward initiatives to reform both control decisions with risk consequences and correct-by-design paradigms for performance reliability associated with the class of stochastic linear dynamical systems with integral quadratic costs and subject to network delays, control and communication constraints.
