A Dual Gradient-projection Method for Large-scale Strictly Convex Quadratic Problems PDF Download
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Languages : en
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Author: Zdenek Dostál
Publisher: Springer Science & Business Media
ISBN: 0387848061
Category : Mathematics
Languages : en
Pages : 293
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Book Description
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: Hongchao Zhang
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Languages : en
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Finally, we propose a class of self-adaptive proximal point methods suitable for degenerate optimization problems where multiple minimizers may exist, or where the Hessian may be singular at a local minimizer. Two different acceptance criteria for an approximate solution to the proximal problem is analyzed and the convergence rate are analogous to those of exact iterates. The second part of this dissertation discusses using gradient methods to solve large-scale box constrained optimization. We first discuss the gradient projection methods. Then, an active set algorithm (ASA) for box constrained optimization is developed. The algorithm consists of a nonmonotone gradient projection step, an unconstrained optimization step, and a set of rules for branching between the two steps. Global convergence to a stationary point is established. Under the strong second-order sufficient optimality condition, without assuming strict complementarity, the algorithm eventually reduces to unconstrained optimization without restarts. For strongly convex quadratic box constrained optimization, ASA is shown to have finite convergence when a conjugate gradient method is used in the unconstrained optimization step. A specific implementation of ASA is given, which exploits the cyclic Barzilai-Borwein algorithm for the gradient projection step and CG_DESCENT for unconstrained optimization. Numerical experiments using the box constrained problems in the CUTEr and MINPACK test problem libraries show that this new algorithm outperforms benchmark softwares such as GENCAN, L-BFGS-B, and TRON.
Author: A. R. Conn
Publisher: SIAM
ISBN: 0898714605
Category : Mathematics
Languages : en
Pages : 960
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Book Description
Mathematics of Computing -- General.
Author: Thomas Frederick Coleman
Publisher: SIAM
ISBN: 9780898712681
Category : Mathematics
Languages : en
Pages : 278
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Book Description
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: Gianni Pillo
Publisher: Springer Science & Business Media
ISBN: 1475732260
Category : Mathematics
Languages : en
Pages : 484
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Book Description
This volume contains the edited texts of the lectures presented at the Workshop on Nonlinear Optimization held in Erice, Sicily, at the "G. Stampacchia" School of Mathematics of the "E. Majorana" Centre for Scientific Culture, June 23 -July 2, 1998. In the tradition of these meetings, the main purpose was to review and discuss recent advances and promising research trends concerning theory, algorithms and innovative applications in the field of Nonlinear Optimization, and of related topics such as Convex Optimization, Nonsmooth Optimization, Variational Inequalities and Complementarity Problems. The meeting was attended by 83 people from 21 countries. Besides the lectures, several formal and informal discussions took place. The result was a wide and deep knowledge of the present research tendencies in the field. We wish to express our appreciation for the active contribution of all the par ticipants in the meeting. Our gratitude is due to the Ettore Majorana Centre in Erice, which offered its facilities and rewarding environment: its staff was certainly instrumental for the success of the meeting. Our gratitude is also due to Francisco Facchinei and Massimo Roma for the effort and time devoted as members of the Organising Committee. We are indebted to the Italian National Research Council, and in particular to the Group on Functional Analysis and its Applications and to the Committees on Engineering Sciences and on Information Sciences and Technolo gies for their financial support. Finally, we address our thanks to Kluwer Academic Publishers for having offered to publish this volume.
Author: Renato de Leone
Publisher: Springer Science & Business Media
ISBN: 1461332796
Category : Mathematics
Languages : en
Pages : 379
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Book Description
This book contains a selection of papers presented at the conference on High Performance Software for Nonlinear Optimization (HPSN097) which was held in Ischia, Italy, in June 1997. The rapid progress of computer technologies, including new parallel architec tures, has stimulated a large amount of research devoted to building software environments and defining algorithms able to fully exploit this new computa tional power. In some sense, numerical analysis has to conform itself to the new tools. The impact of parallel computing in nonlinear optimization, which had a slow start at the beginning, seems now to increase at a fast rate, and it is reasonable to expect an even greater acceleration in the future. As with the first HPSNO conference, the goal of the HPSN097 conference was to supply a broad overview of the more recent developments and trends in nonlinear optimization, emphasizing the algorithmic and high performance software aspects. Bringing together new computational methodologies with theoretical ad vances and new computer technologies is an exciting challenge that involves all scientists willing to develop high performance numerical software. This book contains several important contributions from different and com plementary standpoints. Obviously, the articles in the book do not cover all the areas of the conference topic or all the most recent developments, because of the large number of new theoretical and computational ideas of the last few years.
Author: Amir Beck
Publisher: SIAM
ISBN: 1611974984
Category : Mathematics
Languages : en
Pages : 476
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Book Description
The primary goal of this book is to provide a self-contained, comprehensive study of the main ?rst-order methods that are frequently used in solving large-scale problems. First-order methods exploit information on values and gradients/subgradients (but not Hessians) of the functions composing the model under consideration. With the increase in the number of applications that can be modeled as large or even huge-scale optimization problems, there has been a revived interest in using simple methods that require low iteration cost as well as low memory storage. The author has gathered, reorganized, and synthesized (in a unified manner) many results that are currently scattered throughout the literature, many of which cannot be typically found in optimization books. First-Order Methods in Optimization offers comprehensive study of first-order methods with the theoretical foundations; provides plentiful examples and illustrations; emphasizes rates of convergence and complexity analysis of the main first-order methods used to solve large-scale problems; and covers both variables and functional decomposition methods.
Author: Daniel P. Palomar
Publisher: Cambridge University Press
ISBN: 0521762227
Category : Computers
Languages : en
Pages : 513
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Book Description
Leading experts provide the theoretical underpinnings of the subject plus tutorials on a wide range of applications, from automatic code generation to robust broadband beamforming. Emphasis on cutting-edge research and formulating problems in convex form make this an ideal textbook for advanced graduate courses and a useful self-study guide.
Author: Stephen P. Boyd
Publisher: Cambridge University Press
ISBN: 9780521833783
Category : Business & Economics
Languages : en
Pages : 744
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Book Description
Convex optimization problems arise frequently in many different fields. This book provides a comprehensive introduction to the subject, and shows in detail how such problems can be solved numerically with great efficiency. The book begins with the basic elements of convex sets and functions, and then describes various classes of convex optimization problems. Duality and approximation techniques are then covered, as are statistical estimation techniques. Various geometrical problems are then presented, and there is detailed discussion of unconstrained and constrained minimization problems, and interior-point methods. The focus of the book is on recognizing convex optimization problems and then finding the most appropriate technique for solving them. It contains many worked examples and homework exercises and will appeal to students, researchers and practitioners in fields such as engineering, computer science, mathematics, statistics, finance and economics.
