Large-scale Optimization — Problems and Methods

✍ Scribed by Vladimir Tsurkov (auth.)

Publisher: Springer US
Year: 2001
Tongue: English
Leaves: 321
Series: Applied Optimization 51
Edition: 1
Category: Library

No coin nor oath required. For personal study only.

✦ Synopsis

Decomposition methods aim to reduce large-scale problems to simpler problems. This monograph presents selected aspects of the dimension-reduction problem. Exact and approximate aggregations of multidimensional systems are developed and from a known model of input-output balance, aggregation methods are categorized. The issues of loss of accuracy, recovery of original variables (disaggregation), and compatibility conditions are analyzed in detail. The method of iterative aggregation in large-scale problems is studied. For fixed weights, successively simpler aggregated problems are solved and the convergence of their solution to that of the original problem is analyzed. An introduction to block integer programming is considered. Duality theory, which is widely used in continuous block programming, does not work for the integer problem. A survey of alternative methods is presented and special attention is given to combined methods of decomposition. Block problems in which the coupling variables do not enter the binding constraints are studied. These models are worthwhile because they permit a decomposition with respect to primal and dual variables by two-level algorithms instead of three-level algorithms.
Audience: This book is addressed to specialists in operations research, optimization, and optimal control.

✦ Table of Contents

Front Matter....Pages i-xi
Exact and Approximate Aggregation....Pages 1-76
Iterative Aggregation....Pages 77-128
Introduction to Block Integer Programming....Pages 129-262
Block Problems with a Special Condition for Coupling Variables....Pages 263-300
Back Matter....Pages 301-311

✦ Subjects

Optimization; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Mathematical Modeling and Industrial Mathematics

📜 SIMILAR VOLUMES

Large-Scale Optimization with Applicatio

📁 Large-Scale Optimization with Applications: Part I: Optimization in Inverse Problems and Design

✍ John W. Bandler, Radek M. Biernacki (auth.), Lorenz T. Biegler, Thomas F. Colema 📂 Library 📅 1997 🏛 Springer-Verlag New York 🌐 English

Inverse problems and optimal design have come of age as a consequence of the availability of better, more accurate, and more efficient simulation packages. Many of these simulators, which can run on small workstations, can capture the complicated behavior of the physical systems they are modeling

Large-Scale and Distributed Optimization

📁 Large-Scale and Distributed Optimization

✍ Pontus Giselsson, Anders Rantzer 📂 Library 📅 2018 🏛 Springer International Publishing 🌐 English

This book presents tools and methods for large-scale and distributed optimization. Since many methods in "Big Data" fields rely on solving large-scale optimization problems, often in distributed fashion, this topic has over the last decade emerged to become very important. As well as specific cov

Large-scale and distributed optimization

📁 Large-scale and distributed optimization

✍ Giselsson, Pontus.; Rantzer, Anders (ed.) 📂 Library 📅 2018 🏛 Springer International Publishing : Imprint: Sprin 🌐 English

This book presents tools and methods for large-scale and distributed optimization. Since many methods in "Big Data" fields rely on solving large-scale optimization problems, often in distributed fashion, this topic has over the last decade emerged to become very important. As well as specific covera

Numerical Methods for Bifurcation Proble

📁 Numerical Methods for Bifurcation Problems and Large-Scale Dynamical Systems

✍ V. Balakotaiah, J. Khinast (auth.), Eusebius Doedel, Laurette S. Tuckerman (eds. 📂 Library 📅 2000 🏛 Springer-Verlag New York 🌐 English

The Institute for Mathematics and its Applications (IMA) devoted its 1997-1998 program to Emerging Applications of Dynamical Systems. Dynamical systems theory and related numerical algorithms provide powerful tools for studying the solution behavior of differential equations and mappings. In the pas

Large-scale nonlinear optimization

📁 Large-scale nonlinear optimization

✍ Di Pillo G., Roma M. (eds.) 📂 Library 📅 2006 🏛 Springer 🌐 English

This book reviews and discusses recent advances in the development of methods and algorithms for nonlinear optimization and its applications, focusing on the large-dimensional case, the current forefront of much research. Individual chapters, contributed by eminent authorities, provide an up-to-date

Large-Scale Nonlinear Optimization

📁 Large-Scale Nonlinear Optimization

✍ Nicolas Bérend, J. Frédéric Bonnans (auth.), G. Di Pillo, M. Roma (eds.) 📂 Library 📅 2006 🏛 Springer US 🌐 English

Large-Scale Nonlinear Optimization reviews and discusses recent advances in the development of methods and algorithms for nonlinear optimization and its applications, focusing on the large-dimensional case, the current forefront of much research.The chapters of t