Methods Of Nonsmooth Optimization In Stochastic Programming
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Methods Of Nonsmooth Optimization In Stochastic Programming
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Author : Wim Stefanus van Ackooij
language : en
Publisher: Springer Nature
Release Date : 2025-05-05
Methods Of Nonsmooth Optimization In Stochastic Programming written by Wim Stefanus van Ackooij and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-05-05 with Business & Economics categories.
This book presents a comprehensive series of methods in nonsmooth optimization, with a particular focus on their application in stochastic programming and dedicated algorithms for decision-making under uncertainty. Each method is accompanied by rigorous mathematical analysis, ensuring a deep understanding of the underlying principles. The theoretical discussions included are essential for comprehending the mechanics of various algorithms and the nature of the solutions they provide—whether they are global, local, stationary, or critical. The book begins by introducing fundamental tools from set-valued analysis, optimization, and probability theory. It then transitions from deterministic to stochastic optimization, starting with a thorough discussion of modeling, understanding uncertainty, and incorporating it into optimization problems. Following this foundation, the book explores numerical algorithms for nonsmooth optimization, covering well-known decomposition techniques and algorithms for convex optimization, mixed-integer convex programming, and nonconvex optimization. Additionally, it introduces numerical algorithms specifically for stochastic programming, focusing on stochastic programming with recourse, chance-constrained optimization, and detailed algorithms for both risk-neutral and risk-averse multistage stochastic programs. The book guides readers through the entire process, from defining optimization models for practical problems to presenting implementable algorithms that can be applied in practice. It is intended for students, practitioners, and scholars who may be unfamiliar with stochastic programming and nonsmooth optimization. The analyses provided are also valuable for practitioners who may not be interested in convergence proofs but wish to understand the nature of the solutions obtained.
Practical Methods Of Optimization
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Author : R. Fletcher
language : en
Publisher: John Wiley & Sons
Release Date : 2013-06-06
Practical Methods Of Optimization written by R. Fletcher 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 2013-06-06 with Mathematics categories.
Fully describes optimization methods that are currently most valuable in solving real-life problems. Since optimization has applications in almost every branch of science and technology, the text emphasizes their practical aspects in conjunction with the heuristics useful in making them perform more reliably and efficiently. To this end, it presents comparative numerical studies to give readers a feel for possibile applications and to illustrate the problems in assessing evidence. Also provides theoretical background which provides insights into how methods are derived. This edition offers revised coverage of basic theory and standard techniques, with updated discussions of line search methods, Newton and quasi-Newton methods, and conjugate direction methods, as well as a comprehensive treatment of restricted step or trust region methods not commonly found in the literature. Also includes recent developments in hybrid methods for nonlinear least squares; an extended discussion of linear programming, with new methods for stable updating of LU factors; and a completely new section on network programming. Chapters include computer subroutines, worked examples, and study questions.
Nonsmooth Approach To Optimization Problems With Equilibrium Constraints
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Author : Jiri Outrata
language : en
Publisher: Springer Science & Business Media
Release Date : 1998-07-31
Nonsmooth Approach To Optimization Problems With Equilibrium Constraints written by Jiri Outrata 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 1998-07-31 with Business & Economics categories.
This book presents an in-depth study and a solution technique for an important class of optimization problems. This class is characterized by special constraints: parameter-dependent convex programs, variational inequalities or complementarity problems. All these so-called equilibrium constraints are mostly treated in a convenient form of generalized equations. The book begins with a chapter on auxiliary results followed by a description of the main numerical tools: a bundle method of nonsmooth optimization and a nonsmooth variant of Newton's method. Following this, stability and sensitivity theory for generalized equations is presented, based on the concept of strong regularity. This enables one to apply the generalized differential calculus for Lipschitz maps to derive optimality conditions and to arrive at a solution method. A large part of the book focuses on applications coming from continuum mechanics and mathematical economy. A series of nonacademic problems is introduced and analyzed in detail. Each problem is accompanied with examples that show the efficiency of the solution method. This book is addressed to applied mathematicians and engineers working in continuum mechanics, operations research and economic modelling. Students interested in optimization will also find the book useful.
Encyclopedia Of Optimization
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Author : Christodoulos A. Floudas
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-09-04
Encyclopedia Of Optimization written by Christodoulos A. Floudas 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 2008-09-04 with Mathematics categories.
The goal of the Encyclopedia of Optimization is to introduce the reader to a complete set of topics that show the spectrum of research, the richness of ideas, and the breadth of applications that has come from this field. The second edition builds on the success of the former edition with more than 150 completely new entries, designed to ensure that the reference addresses recent areas where optimization theories and techniques have advanced. Particularly heavy attention resulted in health science and transportation, with entries such as "Algorithms for Genomics", "Optimization and Radiotherapy Treatment Design", and "Crew Scheduling".
Lectures On Convex Optimization
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Author : Yurii Nesterov
language : en
Publisher: Springer
Release Date : 2018-11-19
Lectures On Convex Optimization written by Yurii Nesterov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-19 with Mathematics categories.
This book provides a comprehensive, modern introduction to convex optimization, a field that is becoming increasingly important in applied mathematics, economics and finance, engineering, and computer science, notably in data science and machine learning. Written by a leading expert in the field, this book includes recent advances in the algorithmic theory of convex optimization, naturally complementing the existing literature. It contains a unified and rigorous presentation of the acceleration techniques for minimization schemes of first- and second-order. It provides readers with a full treatment of the smoothing technique, which has tremendously extended the abilities of gradient-type methods. Several powerful approaches in structural optimization, including optimization in relative scale and polynomial-time interior-point methods, are also discussed in detail. Researchers in theoretical optimization as well as professionals working on optimization problems will find this book very useful. It presents many successful examples of how to develop very fast specialized minimization algorithms. Based on the author’s lectures, it can naturally serve as the basis for introductory and advanced courses in convex optimization for students in engineering, economics, computer science and mathematics.
Numerical Nonsmooth Optimization
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Author : Adil M. Bagirov
language : en
Publisher: Springer Nature
Release Date : 2020-02-28
Numerical Nonsmooth Optimization written by Adil M. Bagirov and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-02-28 with Business & Economics categories.
Solving nonsmooth optimization (NSO) problems is critical in many practical applications and real-world modeling systems. The aim of this book is to survey various numerical methods for solving NSO problems and to provide an overview of the latest developments in the field. Experts from around the world share their perspectives on specific aspects of numerical NSO. The book is divided into four parts, the first of which considers general methods including subgradient, bundle and gradient sampling methods. In turn, the second focuses on methods that exploit the problem’s special structure, e.g. algorithms for nonsmooth DC programming, VU decomposition techniques, and algorithms for minimax and piecewise differentiable problems. The third part considers methods for special problems like multiobjective and mixed integer NSO, and problems involving inexact data, while the last part highlights the latest advancements in derivative-free NSO. Given its scope, the book is ideal for students attending courses on numerical nonsmooth optimization, for lecturers who teach optimization courses, and for practitioners who apply nonsmooth optimization methods in engineering, artificial intelligence, machine learning, and business. Furthermore, it can serve as a reference text for experts dealing with nonsmooth optimization.
Handbook Of Simulation Optimization
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Author : Michael C Fu
language : en
Publisher: Springer
Release Date : 2014-11-13
Handbook Of Simulation Optimization written by Michael C Fu and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-13 with Business & Economics categories.
The Handbook of Simulation Optimization presents an overview of the state of the art of simulation optimization, providing a survey of the most well-established approaches for optimizing stochastic simulation models and a sampling of recent research advances in theory and methodology. Leading contributors cover such topics as discrete optimization via simulation, ranking and selection, efficient simulation budget allocation, random search methods, response surface methodology, stochastic gradient estimation, stochastic approximation, sample average approximation, stochastic constraints, variance reduction techniques, model-based stochastic search methods and Markov decision processes. This single volume should serve as a reference for those already in the field and as a means for those new to the field for understanding and applying the main approaches. The intended audience includes researchers, practitioners and graduate students in the business/engineering fields of operations research, management science, operations management and stochastic control, as well as in economics/finance and computer science.
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.
System Modelling And Optimization
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Author : J. Dolezal
language : en
Publisher: Springer
Release Date : 2013-06-05
System Modelling And Optimization written by J. Dolezal and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-05 with Computers categories.
Proceedings volume contains carefully selected papers presented during the 17th IFIP Conference on System Modelling and Optimization. Optimization theory and practice, optimal control, system modelling, stochastic optimization, and technical and non-technical applications of the existing theory are among areas mostly addressed in the included papers. Main directions are treated in addition to several survey papers based on invited presentations of leading specialists in the respective fields. Publication provides state-of-the-art in the area of system theory and optimization and points out several new areas (e.g fuzzy set, neural nets), where classical optimization topics intersects with computer science methodology.
Mathematics Of Operations Research
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Author :
language : en
Publisher:
Release Date : 1991
Mathematics Of Operations Research written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Mathematics categories.
Articles of mathematical interest as well as operations research and management science.