Special Issue On Mathematical Programming With Data Perturbations
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Special Issue On Mathematical Programming With Data Perturbations
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Author : Anthony V. Fiacco
language : en
Publisher:
Release Date : 1986
Special Issue On Mathematical Programming With Data Perturbations written by Anthony V. Fiacco and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with categories.
Mathematical Programming With Data Perturbations
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Author : Anthony V. Fiacco
language : en
Publisher: CRC Press
Release Date : 2020-09-24
Mathematical Programming With Data Perturbations written by Anthony V. Fiacco and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-24 with Mathematics categories.
Presents research contributions and tutorial expositions on current methodologies for sensitivity, stability and approximation analyses of mathematical programming and related problem structures involving parameters. The text features up-to-date findings on important topics, covering such areas as the effect of perturbations on the performance of algorithms, approximation techniques for optimal control problems, and global error bounds for convex inequalities.
Mathematical Programming With Data Perturbations
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Author : Anthony V. Fiacco
language : en
Publisher: CRC Press
Release Date : 2020-09-23
Mathematical Programming With Data Perturbations written by Anthony V. Fiacco and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-23 with Mathematics categories.
Presents research contributions and tutorial expositions on current methodologies for sensitivity, stability and approximation analyses of mathematical programming and related problem structures involving parameters. The text features up-to-date findings on important topics, covering such areas as the effect of perturbations on the performance of algorithms, approximation techniques for optimal control problems, and global error bounds for convex inequalities.
Mathematical Programming With Data Perturbations Ii Second Edition
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Author : Fiacco
language : en
Publisher: CRC Press
Release Date : 2020-09-24
Mathematical Programming With Data Perturbations Ii Second Edition written by Fiacco and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-24 with Mathematics categories.
This book presents theoretical results, including an extension of constant rank and implicit function theorems, continuity and stability bounds results for infinite dimensional problems, and the interrelationship between optimal value conditions and shadow prices for stable and unstable programs.
Quadratic Programming And Affine Variational Inequalities
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Author : Gue Myung Lee
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-03-30
Quadratic Programming And Affine Variational Inequalities written by Gue Myung Lee 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 2006-03-30 with Mathematics categories.
Quadratic programs and affine variational inequalities represent two fundamental, closely-related classes of problems in the t,heories of mathematical programming and variational inequalities, resp- tively. This book develops a unified theory on qualitative aspects of nonconvex quadratic programming and affine variational inequ- ities. The first seven chapters introduce the reader step-by-step to the central issues concerning a quadratic program or an affine variational inequality, such as the solution existence, necessary and sufficient conditions for a point to belong to the solution set, and properties of the solution set. The subsequent two chapters discuss briefly two concrete nlodels (linear fractional vector optimization and the traffic equilibrium problem) whose analysis can benefit a lot from using the results on quadratic programs and affine variational inequalities. There are six chapters devoted to the study of conti- ity and/or differentiability properties of the characteristic maps and functions in quadratic programs and in affine variational inequa- ties where all the components of the problem data are subject to perturbation. Quadratic programs and affine variational inequa- ties under linear perturbations are studied in three other chapters. One special feature of the presentation is that when a certain pr- erty of a characteristic map or function is investigated, we always try first to establish necessary conditions for it to hold, then we go on to study whether the obtained necessary conditions are suf- cient ones. This helps to clarify the structures of the two classes of problems under consideration.
Optimization With Data Perturbations Ii
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Author : Doug E. Ward
language : en
Publisher:
Release Date : 2001
Optimization With Data Perturbations Ii written by Doug E. Ward and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematical optimization categories.
Perturbations Optimization And Statistics
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Author : Tamir Hazan
language : en
Publisher: MIT Press
Release Date : 2016-12-23
Perturbations Optimization And Statistics written by Tamir Hazan and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-23 with Computers categories.
A description of perturbation-based methods developed in machine learning to augment novel optimization methods with strong statistical guarantees. In nearly all machine learning, decisions must be made given current knowledge. Surprisingly, making what is believed to be the best decision is not always the best strategy, even when learning in a supervised learning setting. An emerging body of work on learning under different rules applies perturbations to decision and learning procedures. These methods provide simple and highly efficient learning rules with improved theoretical guarantees. This book describes perturbation-based methods developed in machine learning to augment novel optimization methods with strong statistical guarantees, offering readers a state-of-the-art overview. Chapters address recent modeling ideas that have arisen within the perturbations framework, including Perturb & MAP, herding, and the use of neural networks to map generic noise to distribution over highly structured data. They describe new learning procedures for perturbation models, including an improved EM algorithm and a learning algorithm that aims to match moments of model samples to moments of data. They discuss understanding the relation of perturbation models to their traditional counterparts, with one chapter showing that the perturbations viewpoint can lead to new algorithms in the traditional setting. And they consider perturbation-based regularization in neural networks, offering a more complete understanding of dropout and studying perturbations in the context of deep neural networks.
Relaxation And Decomposition Methods For Mixed Integer Nonlinear Programming
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Author : Ivo Nowak
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-03-28
Relaxation And Decomposition Methods For Mixed Integer Nonlinear Programming written by Ivo Nowak 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 2006-03-28 with Computers categories.
Nonlinearoptimizationproblemscontainingbothcontinuousanddiscretevariables are called mixed integer nonlinear programs (MINLP). Such problems arise in many ?elds, such as process industry, engineering design, communications, and ?nance. There is currently a huge gap between MINLP and mixed integer linear programming(MIP) solvertechnology.With a modernstate-of-the-artMIP solver itispossibletosolvemodelswithmillionsofvariablesandconstraints,whereasthe dimensionofsolvableMINLPsisoftenlimitedbyanumberthatissmallerbythree or four orders of magnitude. It is theoretically possible to approximate a general MINLP by a MIP with arbitrary precision. However, good MIP approximations are usually much larger than the original problem. Moreover, the approximation of nonlinear functions by piecewise linear functions can be di?cult and ti- consuming. In this book relaxation and decomposition methods for solving nonconvex structured MINLPs are proposed. In particular, a generic branch-cut-and-price (BCP) framework for MINLP is presented. BCP is the underlying concept in almost all modern MIP solvers. Providing a powerful decomposition framework for both sequential and parallel solvers, it made the success of the current MIP technology possible. So far generic BCP frameworks have been developed only for MIP, for example,COIN/BCP (IBM, 2003) andABACUS (OREAS GmbH, 1999). In order to generalize MIP-BCP to MINLP-BCP, the following points have to be taken into account: • A given (sparse) MINLP is reformulated as a block-separable program with linear coupling constraints.The block structure makes it possible to generate Lagrangian cuts and to apply Lagrangian heuristics. • In order to facilitate the generation of polyhedral relaxations, nonlinear c- vex relaxations are constructed. • The MINLP separation and pricing subproblems for generating cuts and columns are solved with specialized MINLP solvers.
Mathematical Programming With Data Perturbations I
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Author : Anthony V. Fiacco
language : en
Publisher:
Release Date : 1982
Mathematical Programming With Data Perturbations I written by Anthony V. Fiacco and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with Mathematics categories.
Basic results; Applications and interfaces.
Parametric Optimization And Related Topics Iv
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Author : Jürgen Guddat
language : en
Publisher: Peter Lang Gmbh, Internationaler Verlag Der Wissenschaften
Release Date : 1997
Parametric Optimization And Related Topics Iv written by Jürgen Guddat and has been published by Peter Lang Gmbh, Internationaler Verlag Der Wissenschaften this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematical optimization categories.
This volume contains the proceedings of the fourth conference on Parametric Optimization and Related Topics, held in Enschede, The Netherlands, from June 6-9, 1995. Parametric optimization, as a part of mathematical programming, investigates the behaviour of solutions to optimization problems under data perturbations. Properties involved, such as continuity, differentiability, topological stability and structural stability play a fundamental role in a series of further questions that are of interest both from a practical and a theoretical point of view. Many connections with other disciplines of operations research, like stochastic programming, model-building, numerical methods and optimal control, originate from these properties. The presented papers (all refereed) are topical and original studies reflecting recent results in current directions of research in theory and applications.