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Author : Laurie Ann Hulbert
Publisher :
ISBN 13 :
Total Pages : 288 pages
Book Rating : 4.E/5 ( download)
Download or read book Solving Large Sparse Quadratic Programs with Simple Bounds written by Laurie Ann Hulbert and published by . This book was released on 1990 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Cornell University. Dept. of Computer Science
Publisher :
ISBN 13 :
Total Pages : 36 pages
Book Rating : 4.:/5 (25 download)
Download or read book A Direct Active Set Algorithm for Large Sparse Quadratic Programs with Simple Bounds written by Cornell University. Dept. of Computer Science and published by . This book was released on 1988 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt: We show how a direct active set method for solving definite and indefinite quadratic programs with simple bounds can be efficiently implemented for large sparse problems. All of the necessary factorizations can be carried out in a static data structure that is set up before the numeric computation begins. The space required for these factorizations is no larger than that required for a single sparse Cholesky factorization of a matrix with the same sparsity structure as the Hessian of the quadratic. We propose several improvements to this basic algorithm: a new way to find a search direction in the indefinite case that allows us to free more than one variable at a time and a new heuristic method for finding a starting point. These ideas are motivated by the two-norm trust region problem. Additionally, we also show how projection techniques can be used to add several constraints to the active set at each iteration. Our experimental results show that an algorithm with these improvements runs much faster than the basic algorithm for positive definite problems and finds local minima with lower function values for indefinite problems.
Author : Cornell University. Dept. of Computer Science
Publisher :
ISBN 13 :
Total Pages : 26 pages
Book Rating : 4.:/5 (241 download)
Download or read book A Globally and Superlinearly Convergent Algorithm for Convex Quadratic Programs with Simple Bounds written by Cornell University. Dept. of Computer Science and published by . This book was released on 1990 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt: Keywords: quadratic programming, interior point methods, simple bounds, box constraints, large sparse minimization.
Author : Zdenek Dostál
Publisher : Springer Science & Business Media
ISBN 13 : 0387848061
Total Pages : 293 pages
Book Rating : 4.3/5 (878 download)
Download or read book Optimal Quadratic Programming Algorithms written by Zdenek Dostál and published by Springer Science & Business Media. This book was released on 2009-04-03 with total page 293 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quadratic programming (QP) is one advanced mathematical technique that allows for the optimization of a quadratic function in several variables in the presence of linear constraints. This book presents recently developed algorithms for solving large QP problems and focuses on algorithms which are, in a sense optimal, i.e., they can solve important classes of problems at a cost proportional to the number of unknowns. For each algorithm presented, the book details its classical predecessor, describes its drawbacks, introduces modifications that improve its performance, and demonstrates these improvements through numerical experiments. This self-contained monograph can serve as an introductory text on quadratic programming for graduate students and researchers. Additionally, since the solution of many nonlinear problems can be reduced to the solution of a sequence of QP problems, it can also be used as a convenient introduction to nonlinear programming.
Author : Immanuel M. Bomze
Publisher : Springer Science & Business Media
ISBN 13 : 1475726007
Total Pages : 350 pages
Book Rating : 4.4/5 (757 download)
Download or read book Developments in Global Optimization written by Immanuel M. Bomze and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years global optimization has found applications in many interesting areas of science and technology including molecular biology, chemical equilibrium problems, medical imaging and networks. The collection of papers in this book indicates the diverse applicability of global optimization. Furthermore, various algorithmic, theoretical developments and computational studies are presented. Audience: All researchers and students working in mathematical programming.
Author : Ronald Harlan Nickel
Publisher :
ISBN 13 :
Total Pages : 180 pages
Book Rating : 4.:/5 (121 download)
Download or read book A Sequential Quadratic Programming Algorithm for Solving Large, Sparse Nonlinear Programs written by Ronald Harlan Nickel and published by . This book was released on 1984 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: This document describes the structure and theory for a sequential quadratic programming algorithm for solving large, sparse nonlinear optimization problems. Also provided are the details of a computer implementation of the algorithm, along with test results. The algorithm is based on Han's sequential quadratic programming method. It maintains a sparse approximation to the Cholesky factor of the Hessian of the Lagrangian and stores all gradients in a sparse format. The solution to the quadratic program generated at each step is obtained by solving the dual quadratic program using a projected conjugate gradient algorithm. Sine only active constraints are considered in forming the dual, the dual problem will normally be much smaller than the primal quadratic program and, hence, much easier to solve. An updating procedure is employed that does not destroy sparsity. Several test problems, ranging in size from 5 to 60 variables were solved with the algorithm. These results indicate that the algorithm has the potential to solve large, sparse nonlinear programs. The algorithm is especially attractive for solving problems having nonlinear constraints. (Author).
Author : Thomas Frederick Coleman
Publisher : SIAM
ISBN 13 : 9780898712681
Total Pages : 278 pages
Book Rating : 4.7/5 (126 download)
Download or read book Large-scale Numerical Optimization written by Thomas Frederick Coleman and published by SIAM. This book was released on 1990-01-01 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Ake Bjorck
Publisher : SIAM
ISBN 13 : 9781611971484
Total Pages : 425 pages
Book Rating : 4.9/5 (714 download)
Download or read book Numerical Methods for Least Squares Problems written by Ake Bjorck and published by SIAM. This book was released on 1996-01-01 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: The method of least squares was discovered by Gauss in 1795. It has since become the principal tool to reduce the influence of errors when fitting models to given observations. Today, applications of least squares arise in a great number of scientific areas, such as statistics, geodetics, signal processing, and control. In the last 20 years there has been a great increase in the capacity for automatic data capturing and computing. Least squares problems of large size are now routinely solved. Tremendous progress has been made in numerical methods for least squares problems, in particular for generalized and modified least squares problems and direct and iterative methods for sparse problems. Until now there has not been a monograph that covers the full spectrum of relevant problems and methods in least squares. This volume gives an in-depth treatment of topics such as methods for sparse least squares problems, iterative methods, modified least squares, weighted problems, and constrained and regularized problems. The more than 800 references provide a comprehensive survey of the available literature on the subject.
Author : Nicolas Hadjisavvas
Publisher : Springer Science & Business Media
ISBN 13 : 3642566456
Total Pages : 422 pages
Book Rating : 4.6/5 (425 download)
Download or read book Generalized Convexity and Generalized Monotonicity written by Nicolas Hadjisavvas and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: Various generalizations of convex functions have been introduced in areas such as mathematical programming, economics, management science, engineering, stochastics and applied sciences, for example. Such functions preserve one or more properties of convex functions and give rise to models which are more adaptable to real-world situations than convex models. Similarly, generalizations of monotone maps have been studied recently. A growing literature of this interdisciplinary field has appeared, and a large number of international meetings are entirely devoted or include clusters on generalized convexity and generalized monotonicity. The present book contains a selection of refereed papers presented at the 6th International Symposium on Generalized Convexity/Monotonicity, and aims to review the latest developments in the field.
Author : Seyoung Oh
Publisher :
ISBN 13 :
Total Pages : 256 pages
Book Rating : 4.:/5 (319 download)
Download or read book Efficient Methods for Large-scale Sparse Linear and Quadratic Programs written by Seyoung Oh and published by . This book was released on 1992 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Yousef Saad
Publisher : SIAM
ISBN 13 : 0898715342
Total Pages : 537 pages
Book Rating : 4.8/5 (987 download)
Download or read book Iterative Methods for Sparse Linear Systems written by Yousef Saad and published by SIAM. This book was released on 2003-04-01 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- General.
Author : Neculai Andrei
Publisher : Springer
ISBN 13 : 3319583565
Total Pages : 514 pages
Book Rating : 4.3/5 (195 download)
Download or read book Continuous Nonlinear Optimization for Engineering Applications in GAMS Technology written by Neculai Andrei and published by Springer. This book was released on 2017-12-04 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the theoretical details and computational performances of algorithms used for solving continuous nonlinear optimization applications imbedded in GAMS. Aimed toward scientists and graduate students who utilize optimization methods to model and solve problems in mathematical programming, operations research, business, engineering, and industry, this book enables readers with a background in nonlinear optimization and linear algebra to use GAMS technology to understand and utilize its important capabilities to optimize algorithms for modeling and solving complex, large-scale, continuous nonlinear optimization problems or applications. Beginning with an overview of constrained nonlinear optimization methods, this book moves on to illustrate key aspects of mathematical modeling through modeling technologies based on algebraically oriented modeling languages. Next, the main feature of GAMS, an algebraically oriented language that allows for high-level algebraic representation of mathematical optimization models, is introduced to model and solve continuous nonlinear optimization applications. More than 15 real nonlinear optimization applications in algebraic and GAMS representation are presented which are used to illustrate the performances of the algorithms described in this book. Theoretical and computational results, methods, and techniques effective for solving nonlinear optimization problems, are detailed through the algorithms MINOS, KNITRO, CONOPT, SNOPT and IPOPT which work in GAMS technology.
Author : Neculai Andrei
Publisher : Springer Nature
ISBN 13 : 3031087208
Total Pages : 824 pages
Book Rating : 4.0/5 (31 download)
Download or read book Modern Numerical Nonlinear Optimization written by Neculai Andrei and published by Springer Nature. This book was released on 2022-10-18 with total page 824 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 :
Publisher : Stanford University
ISBN 13 :
Total Pages : 128 pages
Book Rating : 4./5 ( download)
Download or read book A Regularized Active-Set method For Sparse Convex Quadratic Programming written by and published by Stanford University. This book was released on with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : D. Butnariu
Publisher : Elsevier
ISBN 13 : 0080508766
Total Pages : 515 pages
Book Rating : 4.0/5 (85 download)
Download or read book Inherently Parallel Algorithms in Feasibility and Optimization and their Applications written by D. Butnariu and published by Elsevier. This book was released on 2001-06-18 with total page 515 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Haifa 2000 Workshop on "Inherently Parallel Algorithms for Feasibility and Optimization and their Applications" brought together top scientists in this area. The objective of the Workshop was to discuss, analyze and compare the latest developments in this fast growing field of applied mathematics and to identify topics of research which are of special interest for industrial applications and for further theoretical study.Inherently parallel algorithms, that is, computational methods which are, by their mathematical nature, parallel, have been studied in various contexts for more than fifty years. However, it was only during the last decade that they have mostly proved their practical usefulness because new generations of computers made their implementation possible in order to solve complex feasibility and optimization problems involving huge amounts of data via parallel processing. These led to an accumulation of computational experience and theoretical information and opened new and challenging questions concerning the behavior of inherently parallel algorithms for feasibility and optimization, their convergence in new environments and in circumstances in which they were not considered before their stability and reliability. Several research groups all over the world focused on these questions and it was the general feeling among scientists involved in this effort that the time has come to survey the latest progress and convey a perspective for further development and concerted scientific investigations. Thus, the editors of this volume, with the support of the Israeli Academy for Sciences and Humanities, took the initiative of organizing a Workshop intended to bring together the leading scientists in the field. The current volume is the Proceedings of the Workshop representing the discussions, debates and communications that took place. Having all that information collected in a single book will provide mathematicians and engineers interested in the theoretical and practical aspects of the inherently parallel algorithms for feasibility and optimization with a tool for determining when, where and which algorithms in this class are fit for solving specific problems, how reliable they are, how they behave and how efficient they were in previous applications. Such a tool will allow software creators to choose ways of better implementing these methods by learning from existing experience.
Author : R. Horst
Publisher : Springer Science & Business Media
ISBN 13 : 1461520258
Total Pages : 891 pages
Book Rating : 4.4/5 (615 download)
Download or read book Handbook of Global Optimization written by R. Horst and published by Springer Science & Business Media. This book was released on 2013-12-11 with total page 891 pages. Available in PDF, EPUB and Kindle. Book excerpt: Global optimization is concerned with the computation and characterization of global optima of nonlinear functions. During the past three decades the field of global optimization has been growing at a rapid pace, and the number of publications on all aspects of global optimization has been increasing steadily. Many applications, as well as new theoretical, algorithmic, and computational contributions have resulted. The Handbook of Global Optimization is the first comprehensive book to cover recent developments in global optimization. Each contribution in the Handbook is essentially expository in nature, but scholarly in its treatment. The chapters cover optimality conditions, complexity results, concave minimization, DC programming, general quadratic programming, nonlinear complementarity, minimax problems, multiplicative programming, Lipschitz optimization, fractional programming, network problems, trajectory methods, homotopy methods, interval methods, and stochastic approaches. The Handbook of Global Optimization is addressed to researchers in mathematical programming, as well as all scientists who use optimization methods to model and solve problems.
Author : Jesse Louis Barlow
Publisher :
ISBN 13 :
Total Pages : 16 pages
Book Rating : 4.:/5 (218 download)
Download or read book Direct Solution of Constrained Quadratic Programming Problems written by Jesse Louis Barlow and published by . This book was released on 1989 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt: The positive definite linear complementary problem is an important special case of the bound constrained problem. If A is an M-matrix, there are simplifications in the implementation of the projected gradient strategy. This new approach allows to use direct solution methods for many large sparse bound constrained least squares problems."
