Stochastic Optimization Methods

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First Order And Stochastic Optimization Methods For Machine Learning
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Author : Guanghui Lan
language : en
Publisher: Springer Nature
Release Date : 2020-05-15
First Order And Stochastic Optimization Methods For Machine Learning written by Guanghui Lan and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-15 with Mathematics categories.
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.
Stochastic Optimization Methods
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Author : Kurt Marti
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-12-05
Stochastic Optimization Methods written by Kurt Marti and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-12-05 with Business & Economics categories.
Optimization problems arising in practice involve random parameters. For the computation of robust optimal solutions, i.e., optimal solutions being insensitive with respect to random parameter variations, deterministic substitute problems are needed. Based on the distribution of the random data, and using decision theoretical concepts, optimization problems under stochastic uncertainty are converted into deterministic substitute problems. Due to the occurring probabilities and expectations, approximative solution techniques must be applied. Deterministic and stochastic approximation methods and their analytical properties are provided: Taylor expansion, regression and response surface methods, probability inequalities, First Order Reliability Methods, convex approximation/deterministic descent directions/efficient points, stochastic approximation methods, differentiation of probability and mean value functions. Convergence results of the resulting iterative solution procedures are given.
Stochastic Optimization
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Author : Stanislav Uryasev
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Stochastic Optimization written by Stanislav Uryasev and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Technology & Engineering categories.
Stochastic programming is the study of procedures for decision making under the presence of uncertainties and risks. Stochastic programming approaches have been successfully used in a number of areas such as energy and production planning, telecommunications, and transportation. Recently, the practical experience gained in stochastic programming has been expanded to a much larger spectrum of applications including financial modeling, risk management, and probabilistic risk analysis. Major topics in this volume include: (1) advances in theory and implementation of stochastic programming algorithms; (2) sensitivity analysis of stochastic systems; (3) stochastic programming applications and other related topics. Audience: Researchers and academies working in optimization, computer modeling, operations research and financial engineering. The book is appropriate as supplementary reading in courses on optimization and financial engineering.
Stochastic Optimization Methods For Modern Machine Learning Problems
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Author : Yuejiao Sun
language : en
Publisher:
Release Date : 2021
Stochastic Optimization Methods For Modern Machine Learning Problems written by Yuejiao Sun and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with categories.
Optimization has been the workhorse of solving machine learning problems. However, the efficiency of these methods remains far from satisfaction to meet the ever-growing demand that arises in modern applications. In this context, the present dissertation will focus on two fundamental classes of machine learning problems: 1) stochastic nested problems, where one subproblem builds upon the solution of others; and, 2) stochastic distributed problems, where the subproblems are coupled through sharing the common variables. One key difficulty of solving stochastic nested problems is that the hierarchically coupled structure makes the computation of (stochastic) gradients, the basic element in first-order optimization machinery, prohibitively expensive or even impossible.We will develop the first stochastic optimization method, which runs in a single-loop manner and achieves the same sample complexity as the stochastic gradient descent method for non-nested problems. One key difficulty of solving stochastic distributed problems is the resource intensity, especially when algorithms are running atresource-limited devices. In this context, we will introduce a class of communication-adaptive stochastic gradient descent (SGD) methods, which adaptively reuse the stale gradients, thus saving communication. We will show that the new algorithms have convergence rates comparable to original SGD and Adam algorithms, but enjoy impressive empirical performance in terms of total communication round reduction.
Stochastic Optimization Methods
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Author : Kurt Marti
language : en
Publisher:
Release Date : 2015
Stochastic Optimization Methods written by Kurt Marti and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with categories.
This book examines optimization problems that in practice involve random model parameters. It details the computation of robust optimal solutions, i.e., optimal solutions that are insensitive with respect to random parameter variations, where appropriate deterministic substitute problems are needed. Based on the probability distribution of the random data, and using decision theoretical concepts, optimization problems under stochastic uncertainty are converted into appropriate deterministic substitute problems. Due to the probabilities and expectations involved, the book also shows how to apply approximative solution techniques. Several deterministic and stochastic approximation methods are provided: Taylor expansion methods, regression and response surface methods (RSM), probability inequalities, multiple linearization of survival/failure domains, discretization methods, convex approximation/deterministic descent directions/efficient points, stochastic approximation and gradient procedures, and differentiation formulas for probabilities and expectations. In the third edition, this book further develops stochastic optimization methods. In particular, it now shows how to apply stochastic optimization methods to the approximate solution of important concrete problems arising in engineering, economics and operations research.
Stochastic Optimization
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Author : Ioannis Dritsas
language : en
Publisher: BoD – Books on Demand
Release Date : 2011-02-28
Stochastic Optimization written by Ioannis Dritsas and has been published by BoD – Books on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-02-28 with Computers categories.
Stochastic Optimization Algorithms have become essential tools in solving a wide range of difficult and critical optimization problems. Such methods are able to find the optimum solution of a problem with uncertain elements or to algorithmically incorporate uncertainty to solve a deterministic problem. They even succeed in fighting uncertainty with uncertainty. This book discusses theoretical aspects of many such algorithms and covers their application in various scientific fields.
Optimization Methods And Applications
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Author : Sergiy Butenko
language : en
Publisher: Springer
Release Date : 2018-02-20
Optimization Methods And Applications written by Sergiy Butenko and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-20 with Mathematics categories.
Researchers and practitioners in computer science, optimization, operations research and mathematics will find this book useful as it illustrates optimization models and solution methods in discrete, non-differentiable, stochastic, and nonlinear optimization. Contributions from experts in optimization are showcased in this book showcase a broad range of applications and topics detailed in this volume, including pattern and image recognition, computer vision, robust network design, and process control in nonlinear distributed systems. This book is dedicated to the 80th birthday of Ivan V. Sergienko, who is a member of the National Academy of Sciences (NAS) of Ukraine and the director of the V.M. Glushkov Institute of Cybernetics. His work has had a significant impact on several theoretical and applied aspects of discrete optimization, computational mathematics, systems analysis and mathematical modeling.
Stochastic Optimization Methods In Finance And Energy
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Author : Marida Bertocchi
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-09-15
Stochastic Optimization Methods In Finance And Energy written by Marida Bertocchi and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-15 with Business & Economics categories.
This volume presents a collection of contributions dedicated to applied problems in the financial and energy sectors that have been formulated and solved in a stochastic optimization framework. The invited authors represent a group of scientists and practitioners, who cooperated in recent years to facilitate the growing penetration of stochastic programming techniques in real-world applications, inducing a significant advance over a large spectrum of complex decision problems. After the recent widespread liberalization of the energy sector in Europe and the unprecedented growth of energy prices in international commodity markets, we have witnessed a significant convergence of strategic decision problems in the energy and financial sectors. This has often resulted in common open issues and has induced a remarkable effort by the industrial and scientific communities to facilitate the adoption of advanced analytical and decision tools. The main concerns of the financial community over the last decade have suddenly penetrated the energy sector inducing a remarkable scientific and practical effort to address previously unforeseeable management problems. Stochastic Optimization Methods in Finance and Energy: New Financial Products and Energy Markets Strategies aims to include in a unified framework for the first time an extensive set of contributions related to real-world applied problems in finance and energy, leading to a common methodological approach and in many cases having similar underlying economic and financial implications. Part 1 of the book presents 6 chapters related to financial applications; Part 2 presents 7 chapters on energy applications; and Part 3 presents 5 chapters devoted to specific theoretical and computational issues.
Stochastic Modeling And Optimization Methods For Critical Infrastructure Protection Volume 2
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Author : Alexei A. Gaivoronski
language : en
Publisher: John Wiley & Sons
Release Date : 2025-05-13
Stochastic Modeling And Optimization Methods For Critical Infrastructure Protection Volume 2 written by Alexei A. Gaivoronski and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-05-13 with Business & Economics categories.
Stochastic Modeling and Optimization Methods for Critical Infrastructure Protection is a thorough exploration of mathematical models and tools that are designed to strengthen critical infrastructures against threats – both natural and adversarial. Divided into two volumes, this first volume examines stochastic modeling across key economic sectors and their interconnections, while the second volume focuses on advanced mathematical methods for enhancing infrastructure protection. The book covers a range of themes, including risk assessment techniques that account for systemic interdependencies within modern technospheres, the dynamics of uncertainty, instability and system vulnerabilities. The book also presents other topics such as cryptographic information protection and Shannon’s theory of secret systems, alongside solutions arising from optimization, game theory and machine learning approaches. Featuring research from international collaborations, this book covers both theory and applications, offering vital insights for advanced risk management curricula. It is intended not only for researchers, but also educators and professionals in infrastructure protection and stochastic optimization.
Optimization Methods In Finance
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Author : Gerard Cornuejols
language : en
Publisher: Cambridge University Press
Release Date : 2006-12-21
Optimization Methods In Finance written by Gerard Cornuejols and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-12-21 with Mathematics categories.
Optimization models play an increasingly important role in financial decisions. This is the first textbook devoted to explaining how recent advances in optimization models, methods and software can be applied to solve problems in computational finance more efficiently and accurately. Chapters discussing the theory and efficient solution methods for all major classes of optimization problems alternate with chapters illustrating their use in modeling problems of mathematical finance. The reader is guided through topics such as volatility estimation, portfolio optimization problems and constructing an index fund, using techniques such as nonlinear optimization models, quadratic programming formulations and integer programming models respectively. The book is based on Master's courses in financial engineering and comes with worked examples, exercises and case studies. It will be welcomed by applied mathematicians, operational researchers and others who work in mathematical and computational finance and who are seeking a text for self-learning or for use with courses.