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Author : Thomas Frederick Coleman,Yuying Li
Publisher : SIAM
Page : 278 pages
File Size : 48,6 Mb
Release : 1990-01-01
Category : Mathematics
ISBN : 0898712688
Papers from a workshop held at Cornell University, Oct. 1989, and sponsored by Cornell's Mathematical Sciences Institute. Annotation copyright Book News, Inc. Portland, Or.
Author : Vladimir Tsurkov
Publisher : Springer Science & Business Media
Page : 322 pages
File Size : 47,6 Mb
Release : 2013-03-09
Category : Computers
ISBN : 9781475732436
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.
Author : Cornell University. Dept. of Computer Science,Thomas Frederick Coleman
Publisher : Unknown
Page : 28 pages
File Size : 53,9 Mb
Release : 1991
Category : Mathematical optimization
ISBN : OCLC:25776267
We give an introductory overview of the field of large-scale numerical optimization; some of the basic research issues and recent developments are described. Our emphasisis on methods, techniques, and practical concerns. We hope this article will be of interest to both users and students of numerical optimization.
Author : Jorge Nocedal,Stephen Wright
Publisher : Springer Science & Business Media
Page : 686 pages
File Size : 47,5 Mb
Release : 2006-12-11
Category : Mathematics
ISBN : 9780387400655
Optimization is an important tool used in decision science and for the analysis of physical systems used in engineering. One can trace its roots to the Calculus of Variations and the work of Euler and Lagrange. This natural and reasonable approach to mathematical programming covers numerical methods for finite-dimensional optimization problems. It begins with very simple ideas progressing through more complicated concepts, concentrating on methods for both unconstrained and constrained optimization.
Author : David A. Wismer
Publisher : McGraw-Hill Companies
Page : 358 pages
File Size : 53,7 Mb
Release : 1971
Category : Mathematics
ISBN : UOM:39015047422830
Author : Pontus Giselsson,Anders Rantzer
Publisher : Springer
Page : 412 pages
File Size : 44,6 Mb
Release : 2018-11-11
Category : Mathematics
ISBN : 9783319974781
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 coverage of this active research field, the book serves as a powerful source of information for practitioners as well as theoreticians. Large-Scale and Distributed Optimization is a unique combination of contributions from leading experts in the field, who were speakers at the LCCC Focus Period on Large-Scale and Distributed Optimization, held in Lund, 14th–16th June 2017. A source of information and innovative ideas for current and future research, this book will appeal to researchers, academics, and students who are interested in large-scale optimization.
Author : Richard Kipp Martin
Publisher : Springer Science & Business Media
Page : 739 pages
File Size : 49,8 Mb
Release : 2012-12-06
Category : Business & Economics
ISBN : 9781461549758
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 de voted to the theory of linear and integer linear optimization. This theory is developed using two simple, but unifying ideas: projection and inverse projec 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 the 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.
Author : Ernest K. Ryu,Wotao Yin
Publisher : Cambridge University Press
Page : 320 pages
File Size : 43,7 Mb
Release : 2022-12-01
Category : Mathematics
ISBN : 9781009191067
Starting from where a first course in convex optimization leaves off, this text presents a unified analysis of first-order optimization methods – including parallel-distributed algorithms – through the abstraction of monotone operators. With the increased computational power and availability of big data over the past decade, applied disciplines have demanded that larger and larger optimization problems be solved. This text covers the first-order convex optimization methods that are uniquely effective at solving these large-scale optimization problems. Readers will have the opportunity to construct and analyze many well-known classical and modern algorithms using monotone operators, and walk away with a solid understanding of the diverse optimization algorithms. Graduate students and researchers in mathematical optimization, operations research, electrical engineering, statistics, and computer science will appreciate this concise introduction to the theory of convex optimization algorithms.
Author : Gianni Pillo,Massimo Roma
Publisher : Springer
Page : 0 pages
File Size : 40,6 Mb
Release : 2011-02-11
Category : Mathematics
ISBN : 1441940146
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 overview of the field from different and complementary standpoints, including theoretical analysis, algorithmic development, implementation issues and applications.
Author : Subhendu Bikash Hazra
Publisher : Springer Science & Business Media
Page : 216 pages
File Size : 49,6 Mb
Release : 2009-12-16
Category : Mathematics
ISBN : 9783642015021
With continuous development of modern computing hardware and applicable - merical methods, computational ?uid dynamics (CFD) has reached certain level of maturity so that it is being used routinely by scientists and engineers for ?uid ?ow analysis. Since most of the real-life applications involve some kind of optimization, it has been natural to extend the use of CFD tools from ?ow simulation to simu- tion based optimization. However, the transition from simulation to optimization is not straight forward, it requires proper interaction between advanced CFD meth- ologies and state-of-the-art optimization algorithms. The ultimate goal is to achieve optimal solution at the cost of few ?ow solutions. There is growing number of - search activities to achieve this goal. This book results from my work done on simulation based optimization problems at the Department of Mathematics, University of Trier, and reported in my postd- toral thesis (”Habilitationsschrift”) accepted by the Faculty-IV of this University in 2008. The focus of the work has been to develop mathematical methods and - gorithms which lead to ef?cient and high performance computational techniques to solve such optimization problems in real-life applications. Systematic development of the methods and algorithms are presented here. Practical aspects of implemen- tions are discussed at each level as the complexity of the problems increase, suppo- ing with enough number of computational examples.
Author : Gianni Pillo,Massimo Roma
Publisher : Springer Science & Business Media
Page : 297 pages
File Size : 43,5 Mb
Release : 2006-06-03
Category : Mathematics
ISBN : 9780387300658
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 overview of the field from different and complementary standpoints, including theoretical analysis, algorithmic development, implementation issues and applications.
Author : William W. Hager,D.W. Hearn,Panos M. Pardalos
Publisher : Springer Science & Business Media
Page : 470 pages
File Size : 53,5 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461336327
On February 15-17, 1993, a conference on Large Scale Optimization, hosted by the Center for Applied Optimization, was held at the University of Florida. The con ference was supported by the National Science Foundation, the U. S. Army Research Office, and the University of Florida, with endorsements from SIAM, MPS, ORSA and IMACS. Forty one invited speakers presented papers on mathematical program ming and optimal control topics with an emphasis on algorithm development, real world applications and numerical results. Participants from Canada, Japan, Sweden, The Netherlands, Germany, Belgium, Greece, and Denmark gave the meeting an important international component. At tendees also included representatives from IBM, American Airlines, US Air, United Parcel Serice, AT & T Bell Labs, Thinking Machines, Army High Performance Com puting Research Center, and Argonne National Laboratory. In addition, the NSF sponsored attendance of thirteen graduate students from universities in the United States and abroad. Accurate modeling of scientific problems often leads to the formulation of large scale optimization problems involving thousands of continuous and/or discrete vari ables. Large scale optimization has seen a dramatic increase in activities in the past decade. This has been a natural consequence of new algorithmic developments and of the increased power of computers. For example, decomposition ideas proposed by G. Dantzig and P. Wolfe in the 1960's, are now implement able in distributed process ing systems, and today many optimization codes have been implemented on parallel machines.
Author : Neculai Andrei
Publisher : Springer Nature
Page : 824 pages
File Size : 42,5 Mb
Release : 2022-10-18
Category : Mathematics
ISBN : 9783031087202
This book includes a thorough theoretical and computational analysis of unconstrained and constrained optimization algorithms and combines and integrates the most recent techniques and advanced computational linear algebra methods. Nonlinear optimization methods and techniques have reached their maturity and an abundance of optimization algorithms are available for which both the convergence properties and the numerical performances are known. This clear, friendly, and rigorous exposition discusses the theory behind the nonlinear optimization algorithms for understanding their properties and their convergence, enabling the reader to prove the convergence of his/her own algorithms. It covers cases and computational performances of the most known modern nonlinear optimization algorithms that solve collections of unconstrained and constrained optimization test problems with different structures, complexities, as well as those with large-scale real applications. The book is addressed to all those interested in developing and using new advanced techniques for solving large-scale unconstrained or constrained complex optimization problems. Mathematical programming researchers, theoreticians and practitioners in operations research, practitioners in engineering and industry researchers, as well as graduate students in mathematics, Ph.D. and master in mathematical programming will find plenty of recent information and practical approaches for solving real large-scale optimization problems and applications.
Author : Anonim
Publisher : Springer Science & Business Media
Page : 234 pages
File Size : 40,9 Mb
Release : 1997
Category : Engineering design
ISBN : 0387982868
Author : Lorenz T. Biegler,Omar Ghattas,Matthias Heinkenschloss,Bart van Bloemen Waanders
Publisher : Springer Science & Business Media
Page : 347 pages
File Size : 47,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642555084
Optimal design, optimal control, and parameter estimation of systems governed by partial differential equations (PDEs) give rise to a class of problems known as PDE-constrained optimization. The size and complexity of the discretized PDEs often pose significant challenges for contemporary optimization methods. With the maturing of technology for PDE simulation, interest has now increased in PDE-based optimization. The chapters in this volume collectively assess the state of the art in PDE-constrained optimization, identify challenges to optimization presented by modern highly parallel PDE simulation codes, and discuss promising algorithmic and software approaches for addressing them. These contributions represent current research of two strong scientific computing communities, in optimization and PDE simulation. This volume merges perspectives in these two different areas and identifies interesting open questions for further research.
