Very Large Scale Optimization

Author : Pontus Giselsson,Anders Rantzer
Publisher : Springer
Page : 412 pages
File Size : 44,6 Mb
Release : 2018-11-11
Category : Mathematics
ISBN : 9783319974781

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Large-Scale and Distributed Optimization by Pontus Giselsson,Anders Rantzer Pdf

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 : 44,6 Mb
Release : 2012-12-06
Category : Business & Economics
ISBN : 9781461549758

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Large Scale Linear and Integer Optimization: A Unified Approach by Richard Kipp Martin Pdf

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 : Vladimir Tsurkov
Publisher : Springer Science & Business Media
Page : 322 pages
File Size : 43,8 Mb
Release : 2013-03-09
Category : Computers
ISBN : 9781475732436

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Large-scale Optimization by Vladimir Tsurkov Pdf

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 : Jesús M. Velásquez-Bermúdez,Marzieh Khakifirooz,Mahdi Fathi
Publisher : Springer Nature
Page : 282 pages
File Size : 51,7 Mb
Release : 2019-09-06
Category : Mathematics
ISBN : 9783030227883

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Large Scale Optimization in Supply Chains and Smart Manufacturing by Jesús M. Velásquez-Bermúdez,Marzieh Khakifirooz,Mahdi Fathi Pdf

In this book, theory of large scale optimization is introduced with case studies of real-world problems and applications of structured mathematical modeling. The large scale optimization methods are represented by various theories such as Benders’ decomposition, logic-based Benders’ decomposition, Lagrangian relaxation, Dantzig –Wolfe decomposition, multi-tree decomposition, Van Roy’ cross decomposition and parallel decomposition for mathematical programs such as mixed integer nonlinear programming and stochastic programming. Case studies of large scale optimization in supply chain management, smart manufacturing, and Industry 4.0 are investigated with efficient implementation for real-time solutions. The features of case studies cover a wide range of fields including the Internet of things, advanced transportation systems, energy management, supply chain networks, service systems, operations management, risk management, and financial and sales management. Instructors, graduate students, researchers, and practitioners, would benefit from this book finding the applicability of large scale optimization in asynchronous parallel optimization, real-time distributed network, and optimizing the knowledge-based expert system for convex and non-convex problems.

Author : Lorenz T. Biegler,Omar Ghattas,Matthias Heinkenschloss,Bart van Bloemen Waanders
Publisher : Springer Science & Business Media
Page : 347 pages
File Size : 48,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642555084

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Large-Scale PDE-Constrained Optimization by Lorenz T. Biegler,Omar Ghattas,Matthias Heinkenschloss,Bart van Bloemen Waanders Pdf

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.

Author : Martin Grötschel,Sven O. Krumke,Joerg Rambau
Publisher : Springer Science & Business Media
Page : 789 pages
File Size : 54,7 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9783662043318

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Online Optimization of Large Scale Systems by Martin Grötschel,Sven O. Krumke,Joerg Rambau Pdf

In its thousands of years of history, mathematics has made an extraordinary ca reer. It started from rules for bookkeeping and computation of areas to become the language of science. Its potential for decision support was fully recognized in the twentieth century only, vitally aided by the evolution of computing and communi cation technology. Mathematical optimization, in particular, has developed into a powerful machinery to help planners. Whether costs are to be reduced, profits to be maximized, or scarce resources to be used wisely, optimization methods are available to guide decision making. Opti mization is particularly strong if precise models of real phenomena and data of high quality are at hand - often yielding reliable automated control and decision proce dures. But what, if the models are soft and not all data are around? Can mathematics help as well? This book addresses such issues, e. g. , problems of the following type: - An elevator cannot know all transportation requests in advance. In which order should it serve the passengers? - Wing profiles of aircrafts influence the fuel consumption. Is it possible to con tinuously adapt the shape of a wing during the flight under rapidly changing conditions? - Robots are designed to accomplish specific tasks as efficiently as possible. But what if a robot navigates in an unknown environment? - Energy demand changes quickly and is not easily predictable over time. Some types of power plants can only react slowly.

Author : Anonim
Publisher : DIANE Publishing
Page : 55 pages
File Size : 43,8 Mb
Release : 2024-07-03
Category : Electronic
ISBN : 9781428995635

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Very large scale optimization by Anonim Pdf

Author : National Aeronautics and Space Adm Nasa
Publisher : Independently Published
Page : 56 pages
File Size : 46,7 Mb
Release : 2018-09-21
Category : Science
ISBN : 1723908657

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Very Large Scale Optimization by National Aeronautics and Space Adm Nasa Pdf

The purpose of this research under the NASA Small Business Innovative Research program was to develop algorithms and associated software to solve very large nonlinear, constrained optimization tasks. Key issues included efficiency, reliability, memory, and gradient calculation requirements. This report describes the general optimization problem, ten candidate methods, and detailed evaluations of four candidates. The algorithm chosen for final development is a modern recreation of a 1960s external penalty function method that uses very limited computer memory and computational time. Although of lower efficiency, the new method can solve problems orders of magnitude larger than current methods. The resulting BIGDOT software has been demonstrated on problems with 50,000 variables and about 50,000 active constraints. For unconstrained optimization, it has solved a problem in excess of 135,000 variables. The method includes a technique for solving discrete variable problems that finds a "good" design, although a theoretical optimum cannot be guaranteed. It is very scalable in that the number of function and gradient evaluations does not change significantly with increased problem size. Test cases are provided to demonstrate the efficiency and reliability of the methods and software.Vanderplaats, Garrett and Townsend, James C. (Technical Monitor)Langley Research CenterVERY LARGE SCALE INTEGRATION; SOFTWARE ENGINEERING; ALGORITHMS; MULTIDISCIPLINARY DESIGN OPTIMIZATION; NONLINEARITY; PENALTY FUNCTION; LAGRANGIAN FUNCTION; MEMORY (COMPUTERS); PROTOTYPES; APPLICATIONS PROGRAMS (COMPUTERS)

Author : Vinod Kumar Chauhan
Publisher : CRC Press
Page : 189 pages
File Size : 44,7 Mb
Release : 2021-11-18
Category : Computers
ISBN : 9781000505610

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Stochastic Optimization for Large-scale Machine Learning by Vinod Kumar Chauhan Pdf

Advancements in the technology and availability of data sources have led to the `Big Data' era. Working with large data offers the potential to uncover more fine-grained patterns and take timely and accurate decisions, but it also creates a lot of challenges such as slow training and scalability of machine learning models. One of the major challenges in machine learning is to develop efficient and scalable learning algorithms, i.e., optimization techniques to solve large scale learning problems. Stochastic Optimization for Large-scale Machine Learning identifies different areas of improvement and recent research directions to tackle the challenge. Developed optimisation techniques are also explored to improve machine learning algorithms based on data access and on first and second order optimisation methods. Key Features: Bridges machine learning and Optimisation. Bridges theory and practice in machine learning. Identifies key research areas and recent research directions to solve large-scale machine learning problems. Develops optimisation techniques to improve machine learning algorithms for big data problems. The book will be a valuable reference to practitioners and researchers as well as students in the field of machine learning.

Author : William W. Hager,D.W. Hearn,Panos M. Pardalos
Publisher : Springer Science & Business Media
Page : 470 pages
File Size : 46,8 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461336327

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Large Scale Optimization by William W. Hager,D.W. Hearn,Panos M. Pardalos Pdf

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 : Gianni Pillo,Massimo Roma
Publisher : Springer
Page : 0 pages
File Size : 46,9 Mb
Release : 2011-02-11
Category : Mathematics
ISBN : 1441940146

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Large-Scale Nonlinear Optimization by Gianni Pillo,Massimo Roma Pdf

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 : Garrett N. Vanderplaats
Publisher : DIANE Publishing
Page : 58 pages
File Size : 49,8 Mb
Release : 2002
Category : Large scale systems
ISBN : NASA:31769000714819

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Very Large Scale Optimization by Garrett N. Vanderplaats Pdf

Author : Thomas Frederick Coleman,Yuying Li
Publisher : SIAM
Page : 278 pages
File Size : 42,7 Mb
Release : 1990-01-01
Category : Mathematics
ISBN : 0898712688

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Large-scale Numerical Optimization by Thomas Frederick Coleman,Yuying Li Pdf

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 : Lorenz T. Biegler
Publisher : Unknown
Page : 0 pages
File Size : 48,6 Mb
Release : 2024-07-03
Category : Electronic
ISBN : OCLC:875389715

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Large-scale Optimization with Applications by Lorenz T. Biegler Pdf

Author : Lorenz T. Biegler,Thomas Coleman,Andrew r. Conn,Fadil N. Santosa
Publisher : Springer Science & Business Media
Page : 212 pages
File Size : 43,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461206934

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Large-Scale Optimization with Applications by Lorenz T. Biegler,Thomas Coleman,Andrew r. Conn,Fadil N. Santosa Pdf

With contributions by specialists in optimization and practitioners in the fields of aerospace engineering, chemical engineering, and fluid and solid mechanics, the major themes include an assessment of the state of the art in optimization algorithms as well as challenging applications in design and control, in the areas of process engineering and systems with partial differential equation models.