Power system optimization: large-scale c
β Chen, Haoyong; Ngan, Honwing; Zhang, Yongjun
π Library
π
2016
π John Wiley & Sons
π English
β¦ LIBER β¦
π
Large Scale Linear and Integer Optimization: A Unified Approach
β Scribed by Richard Kipp Martin (auth.)
- Publisher
- Springer US
- Year
- 1999
- Tongue
- English
- Leaves
- 736
- Edition
- 1
- Category
- Library
β¬ Acquire This Volume
No coin nor oath required. For personal study only.
β¦ Synopsis
This is a textbook about linear and integer linear optimization. There is a growing need in industries such as airline, trucking, and financial engineering to solve very large linear and integer linear optimization problems. Building these models requires uniquely trained individuals. Not only must they have a thorough understanding of the theory behind mathematical programming, they must have substantial knowledge of how to solve very large models in today's computing environment. The major goal of the book is to develop the theory of linear and integer linear optimization in a unified manner and then demonstrate how to use this theory in a modern computing environment to solve very large real world problems. After presenting introductory material in Part I, Part II of this book is deΒ voted to the theory of linear and integer linear optimization. This theory is developed using two simple, but unifying ideas: projection and inverse projecΒ tion. Through projection we take a system of linear inequalities and replace some of the variables with additional linear inequalities. Inverse projection, the dual of this process, involves replacing linear inequalities with additional variables. Fundamental results such as weak and strong duality, theorems of the alternative, complementary slackness, sensitivity analysis, finite basis theΒ orems, etc. are all explained using projection or inverse projection. Indeed, a unique feature of this book is that these fundamental results are developed and explained before the simplex and interior point algorithms are presented.
β¦ Table of Contents
Front Matter....Pages i-xvii
Front Matter....Pages 1-1
Linear and Integer Linear Optimization....Pages 3-32
Front Matter....Pages 33-33
Linear Systems and Projection....Pages 35-80
Linear Systems and Inverse Projection....Pages 81-101
Integer Linear Systems: Projection and Inverse Projection....Pages 103-139
Front Matter....Pages 141-141
The Simplex Algorithm....Pages 143-181
More on Simplex....Pages 183-217
Interior Point Algorithms: Polyhedral Transformations....Pages 219-260
Interior Point Algorithms: Barrier Methods....Pages 261-311
Integer Programming....Pages 313-346
Front Matter....Pages 347-347
Projection: Bendersβ Decomposition....Pages 349-367
Inverse Projection: Dantzig-Wolfe Decomposition....Pages 369-392
Lagrangian Methods....Pages 393-436
Front Matter....Pages 437-437
Sparse Methods....Pages 439-480
Network Flow Linear Programs....Pages 481-525
Large Integer Programs: Preprocessing and Cutting Planes....Pages 527-564
Large Integer Programs: Projection and Inverse Projection....Pages 565-632
Back Matter....Pages 633-740
β¦ Subjects
Operation Research/Decision Theory; Optimization; Calculus of Variations and Optimal Control; Optimization; Artificial Intelligence (incl. Robotics)
π SIMILAR VOLUMES
Large-Scale and Distributed Optimization
β Pontus Giselsson, Anders Rantzer
π Library
π
2018
π Springer International Publishing
π English
<p>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
β Giselsson, Pontus.; Rantzer, Anders (ed.)
π Library
π
2018
π Springer International Publishing : Imprint: Sprin
π 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
Parallel Algorithms for Optimal Control
β Zoran GajiΔ PhD, Xuemin Shen BSc, MSc, PhD (auth.)
π Library
π
1993
π Springer-Verlag London
π English
<p><B>Parallel Algorithms for Optimal Control of Large Scale </B><B>Linear Systems </B>is a comprehensive presentation for both linear and bilinear systems. The parallel algorithms presented in this book are applicable to a wider class of practical systems than those served by traditional methods fo
Large-scale Optimization β Problems and
β Vladimir Tsurkov (auth.)
π Library
π
2001
π Springer US
π English
<p>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 metho
Generalized Linear Models: A Unified App
β Jeff Gill; Michelle Torres
π Library
π
2019
π SAGE Publications, Incorporated
π English
Generalized Linear Models: A Unified Approach provides an introduction to and overview of GLMs, with each chapter carefully laying the groundwork for the next. Authors Jeff Gill and Michelle Torres provide examples using real data from multiple fields in the social sciences such as psychology, educa