Numerical Methods for Convex Multistage Stochastic Optimization
Numerical Methods for Convex Multistage Stochastic Optimization

Author: Guanghui Lan

Publisher:

Published: 2024-05-22

Total Pages: 0

ISBN-13: 9781638283508

DOWNLOAD EBOOK

Optimization problems involving sequential decisions in a stochastic environment were studied in Stochastic Programming (SP), Stochastic Optimal Control (SOC) and Markov Decision Processes (MDP). This monograph concentrates on SP and SOC modeling approaches. In these frameworks, there are natural situations when the considered problems are convex. The classical approach to sequential optimization is based on dynamic programming. It has the problem of the so-called "curse of dimensionality", in that its computational complexity increases exponentially with respect to the dimension of state variables. Recent progress in solving convex multistage stochastic problems is based on cutting plane approximations of the cost-to-go (value) functions of dynamic programming equations. Cutting plane type algorithms in dynamical settings is one of the main topics of this monograph. Also discussed in this work are stochastic approximation type methods applied to multistage stochastic optimization problems. From the computational complexity point of view, these two types of methods seem to be complimentary to each other. Cutting plane type methods can handle multistage problems with a large number of stages but a relatively smaller number of state (decision) variables. On the other hand, stochastic approximation type methods can only deal with a small number of stages but a large number of decision variables.

First-order and Stochastic Optimization Methods for Machine Learning
First-order and Stochastic Optimization Methods for Machine Learning

Author: Guanghui Lan

Publisher: Springer Nature

Published: 2020-05-15

Total Pages: 591

ISBN-13: 3030395685

DOWNLOAD EBOOK

This book covers not only foundational materials but also the most recent progresses made during the past few years on the area of machine learning algorithms. In spite of the intensive research and development in this area, there does not exist a systematic treatment to introduce the fundamental concepts and recent progresses on machine learning algorithms, especially on those based on stochastic optimization methods, randomized algorithms, nonconvex optimization, distributed and online learning, and projection free methods. This book will benefit the broad audience in the area of machine learning, artificial intelligence and mathematical programming community by presenting these recent developments in a tutorial style, starting from the basic building blocks to the most carefully designed and complicated algorithms for machine learning.

Continuous Optimization
Continuous Optimization

Author: V. Jeyakumar

Publisher: Springer Science & Business Media

Published: 2005-08-10

Total Pages: 476

ISBN-13: 9780387267692

DOWNLOAD EBOOK

The search for the best possible performance is inherent in human nature. Individuals, enterprises and governments all seek optimal—that is, the best—possible solutions of problems that they meet. Evidently, continuous optimization plays an increasingly significant role in everyday management and technical decisions in science, engineering and commerce. The collection of 16 refereed papers in this book covers a diverse number of topics and provides a good picture of recent research in continuous optimization. The first part of the book presents substantive survey articles in a number of important topic areas of continuous optimization. Most of the papers in the second part present results on the theoretical aspects as well as numerical methods of continuous optimization. The papers in the third part are mainly concerned with applications of continuous optimization. Hence, the book will be an additional valuable source of information to faculty, students, and researchers who use continuous optimization to model and solve problems. Audience This book is intended for researchers in mathematical programming, optimization and operations research; engineers in various fields; and graduate students in applied mathematics, engineering and operations research.

Lectures on Stochastic Programming
Lectures on Stochastic Programming

Author: Alexander Shapiro

Publisher: SIAM

Published: 2014-07-09

Total Pages: 512

ISBN-13: 1611973422

DOWNLOAD EBOOK

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.? In?Lectures on Stochastic Programming: Modeling and Theory, Second Edition, the authors introduce new material to reflect recent developments in stochastic programming, including: an analytical description of the tangent and normal cones of chance constrained sets; analysis of optimality conditions applied to nonconvex problems; a discussion of the stochastic dual dynamic programming method; an extended discussion of law invariant coherent risk measures and their Kusuoka representations; and in-depth analysis of dynamic risk measures and concepts of time consistency, including several new results.?

Generalized Bounds for Convex Multistage Stochastic Programs
Generalized Bounds for Convex Multistage Stochastic Programs

Author: Daniel Kuhn

Publisher: Springer Science & Business Media

Published: 2006-03-30

Total Pages: 193

ISBN-13: 3540269010

DOWNLOAD EBOOK

This work was completed during my tenure as a scientific assistant and d- toral student at the Institute for Operations Research at the University of St. Gallen. During that time, I was involved in several industry projects in the field of power management, on the occasion of which I was repeatedly c- fronted with complex decision problems under uncertainty. Although usually hard to solve, I quickly learned to appreciate the benefit of stochastic progr- ming models and developed a strong interest in their theoretical properties. Motivated both by practical questions and theoretical concerns, I became p- ticularly interested in the art of finding tight bounds on the optimal value of a given model. The present work attempts to make a contribution to this important branch of stochastic optimization theory. In particular, it aims at extending some classical bounding methods to broader problem classes of practical relevance. This book was accepted as a doctoral thesis by the University of St. Gallen in June 2004.1 am particularly indebted to Prof. Dr. Karl Frauendorfer for - pervising my work. I am grateful for his kind support in many respects and the generous freedom I received to pursue my own ideas in research. My gratitude also goes to Prof. Dr. Georg Pflug, who agreed to co-chair the dissertation committee. With pleasure I express my appreciation for his encouragement and continuing interest in my work.

Stochastic Decomposition
Stochastic Decomposition

Author: Julia L. Higle

Publisher: Springer Science & Business Media

Published: 2013-11-27

Total Pages: 237

ISBN-13: 1461541158

DOWNLOAD EBOOK

Motivation Stochastic Linear Programming with recourse represents one of the more widely applicable models for incorporating uncertainty within in which the SLP optimization models. There are several arenas model is appropriate, and such models have found applications in air line yield management, capacity planning, electric power generation planning, financial planning, logistics, telecommunications network planning, and many more. In some of these applications, modelers represent uncertainty in terms of only a few seenarios and formulate a large scale linear program which is then solved using LP software. However, there are many applications, such as the telecommunications planning problem discussed in this book, where a handful of seenarios do not capture variability well enough to provide a reasonable model of the actual decision-making problem. Problems of this type easily exceed the capabilities of LP software by several orders of magnitude. Their solution requires the use of algorithmic methods that exploit the structure of the SLP model in a manner that will accommodate large scale applications.

Multistage Stochastic Optimization
Multistage Stochastic Optimization

Author: Georg Ch. Pflug

Publisher: Springer

Published: 2014-11-12

Total Pages: 309

ISBN-13: 3319088432

DOWNLOAD EBOOK

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.

Stochastic Algorithms: Foundations and Applications
Stochastic Algorithms: Foundations and Applications

Author: Osamu Watanabe

Publisher: Springer Science & Business Media

Published: 2009-10-05

Total Pages: 230

ISBN-13: 3642049435

DOWNLOAD EBOOK

The 5th Symposium on Stochastic Algorithms, Foundations and Applications (SAGA 2009) took place during October 26–28, 2009, at Hokkaido University, Sapporo(Japan).ThesymposiumwasorganizedbytheDivisionofComputerS- ence,GraduateSchoolofComputerScienceandTechnology,HokkaidoUniversity. It o?ered the opportunity to present original research on the design and analysis of randomized algorithms, random combinatorialstructures, implem- tation, experimental evaluation and real-world application of stochastic al- rithms/heuristics. In particular, the focus of the SAGA symposia series is on investigating the power of randomization in algorithms, and on the theory of stochastic processes especially within realistic scenarios and applications. Thus, the scope ofthe symposiumrangesfromthe study oftheoreticalfundamentals of randomizedcomputationtoexperimentalinvestigationsonalgorithms/heuristics and related stochastic processes. The SAGA symposium series is a biennial meeting. Previous SAGA s- posiatookplaceinBerlin,Germany(2001,LNCSvol.2264),Hat?eld,UK(2003, LNCS vol. 2827), Moscow, Russia (2005, LNCS vol. 3777), and Zur ¨ ich, Switz- land (2007, LNCS vol. 4665). This year 22 submissions were received, and the Program Committee selected 15 submissions for presentation. All papers were evaluated by at least three members of the ProgramCommittee, partly with the assistance of subreferees. The present volume contains the texts of the 15 papers presented at SAGA 2009, divided into groups of papers on learning, graphs, testing, optimization, and caching as well as on stochastic algorithms in bioinformatics.

Convex and Stochastic Optimization
Convex and Stochastic Optimization

Author: J. Frédéric Bonnans

Publisher: Springer

Published: 2019-04-24

Total Pages: 320

ISBN-13: 3030149773

DOWNLOAD EBOOK

This textbook provides an introduction to convex duality for optimization problems in Banach spaces, integration theory, and their application to stochastic programming problems in a static or dynamic setting. It introduces and analyses the main algorithms for stochastic programs, while the theoretical aspects are carefully dealt with. The reader is shown how these tools can be applied to various fields, including approximation theory, semidefinite and second-order cone programming and linear decision rules. This textbook is recommended for students, engineers and researchers who are willing to take a rigorous approach to the mathematics involved in the application of duality theory to optimization with uncertainty.

Stochastic Programming Methods and Technical Applications
Stochastic Programming Methods and Technical Applications

Author: Kurt Marti

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 448

ISBN-13: 3642457673

DOWNLOAD EBOOK

Optimization problems arising in practice usually contain several random parameters. Hence, in order to obtain optimal solutions being robust with respect to random parameter variations, the mostly available statistical information about the random parameters should be considered already at the planning phase. The original problem with random parameters must be replaced by an appropriate deterministic substitute problem, and efficient numerical solution or approximation techniques have to be developed for those problems. This proceedings volume contains a selection of papers on modelling techniques, approximation methods, numerical solution procedures for stochastic optimization problems and applications to the reliability-based optimization of concrete technical or economic systems.