Author: Stanford University. Department of Operations Research. Systems Optimization LaboratoryPublisher:
ISBN:
Category :
Languages : en
Pages : 34
Book Description
Solving Reduced KKT Systems in Barrier Methods for Linear and Quadratic Programming
Author: Stanford University. Department of Operations Research. Systems Optimization LaboratoryPublisher:
ISBN:
Category :
Languages : en
Pages : 34
Book Description
Stable Reduction to KKT Systems in Barrier Methods for Linear and Quadratic Programming
Author: Stanford University. Engineering-Economic Systems and Operations Research Department. Systems Optimization LaboratoryPublisher:
ISBN:
Category : Linear programming
Languages : en
Pages : 16
Book Description
Abstract: "We discuss methods for solving the key linear equations within primal-dual barrier methods for linear and quadratic programming. Following Freund and Jarre, we explore methods for reducing the Newton equations to 2 X 2 block systems (KKT systems) in a stable manner. Some methods require partitioning the variables into two or more parts, but a simpler approach is derived and recommended. To justify symmetrizing the KKT systems, we assume the use of a sparse solver whose numerical properties are independent of row and column scaling. In particular, we regularize the problem and use indefinite Cholesky-type factorizations. An implementation within OSL is tested on the larger NETLIB examples."
Solving Regularized Linear Programs Using Barrier Methods and KKT Systems
Author: Stanford University. Engineering-Economic Systems and Operations Research Department. Systems Optimization LaboratoryPublisher:
ISBN:
Category : Linear programming
Languages : en
Pages : 18
Book Description
Abstract: "We discuss methods for solving the key linear equations (KKT systems) within primal-dual barrier methods for linear programming. To allow sparse indefinite Cholesky-type factorizations of the KKT systems, we perturb the problem slightly. Perturbations improve the stability of the Cholesky factorizations, but affect the efficiency of the cross-over to simplex (to obtain a basic solution to the original problem). We explore these effects by running OSL on the larger Netlib examples."
A Regularized Active-Set method For Sparse Convex Quadratic Programming
Author: Numerical Analysis 1993
Author: D.F. GriffithsPublisher: CRC Press
ISBN: 1000158055
Category : Mathematics
Languages : en
Pages : 293
Book Description
This volume contains invited papers presented at the 15th Dundee Biennial Conference on Numerical Analysis held at the University of Dundee in June of 1993. The Dundee Conferences are important events in the numerical analysis calendar, and the papers published here represent accounts of recent research work by leading numerical analysts covering a wide range of fields of interest. The book is a valuable guide to the direction of current research in many areas of numerical analysis. It will be of particular interest to graduate students and research workers concerned with the theory and application of numerical methods for solving ordinary and partial differential equations.
Linear Algebra for Large Scale and Real-Time Applications
Author: M.S. MoonenPublisher: Springer Science & Business Media
ISBN: 9401581967
Category : Mathematics
Languages : en
Pages : 434
Book Description
Proceedings of the NATO Advanced Study Institute, Leuven, Belgium, August 3-14, 1992
Convex Optimization in Signal Processing and Communications
Author: Daniel P. PalomarPublisher: Cambridge University Press
ISBN: 0521762227
Category : Computers
Languages : en
Pages : 513
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.
Nonlinear Optimization and Related Topics
Author: Gianni PilloPublisher: Springer Science & Business Media
ISBN: 1475732260
Category : Mathematics
Languages : en
Pages : 484
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.
Linear Programming 1
Author: George B. DantzigPublisher: Springer Science & Business Media
ISBN: 0387226338
Category : Business & Economics
Languages : en
Pages : 462
Book Description
Encompassing all the major topics students will encounter in courses on the subject, the authors teach both the underlying mathematical foundations and how these ideas are implemented in practice. They illustrate all the concepts with both worked examples and plenty of exercises, and, in addition, provide software so that students can try out numerical methods and so hone their skills in interpreting the results. As a result, this will make an ideal textbook for all those coming to the subject for the first time. Authors' note: A problem recently found with the software is due to a bug in Formula One, the third party commercial software package that was used for the development of the interface. It occurs when the date, currency, etc. format is set to a non-United States version. Please try setting your computer date/currency option to the United States option . The new version of Formula One, when ready, will be posted on WWW.
Linear Programming 2
Author: George B. DantzigPublisher: Springer Science & Business Media
ISBN: 0387215697
Category : Mathematics
Languages : en
Pages : 461
Book Description
George Dantzig is widely regarded as the founder of this subject with his invention of the simplex algorithm in the 1940's. In this second volume, the theory of the items discussed in the first volume is expanded to include such additional advanced topics as variants of the simplex method; interior point methods, GUB, decomposition, integer programming, and game theory. Graduate students in the fields of operations research, industrial engineering and applied mathematics will thus find this volume of particular interest.