Solving Reduced KKT Systems in Barrier Methods for Linear and Quadratic Programming PDF Download

Author: Stanford University. Department of Operations Research. Systems Optimization Laboratory
Publisher:
ISBN:
Category :
Languages : en
Pages : 34

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Author: Stanford University. Engineering-Economic Systems and Operations Research Department. Systems Optimization Laboratory
Publisher:
ISBN:
Category : Linear programming
Languages : en
Pages : 16

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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."

Author: Stanford University. Engineering-Economic Systems and Operations Research Department. Systems Optimization Laboratory
Publisher:
ISBN:
Category : Linear programming
Languages : en
Pages : 18

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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."

Author: Stanford University. Department of Operations Research. Systems Optimization Laboratory
Publisher:
ISBN:
Category :
Languages : en
Pages : 142

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Author:
Publisher: Stanford University
ISBN:
Category :
Languages : en
Pages : 128

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Author: Aeneas Marxen
Publisher:
ISBN:
Category : Linear programming
Languages : en
Pages : 86

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Abstract: "The linear program min c[superscript T]x subject to Ax=b, x [greater than or equal to] 0, is solved by the projected Newton barrier method. The method consists of solving a sequence of subproblems of the form [formula] subject to Ax=b. Extensions for upper bounds, free and fixed variables are given. A linear modification is made to the logarithmic barrier function, which results in the solution being bounded in all cases. It also facilitates the provision of a good starting point. The solution of each subproblem involves repeatedly computing a search direction and taking a step along this direction. Ways to find an initial feasible solution, step sizes and convergence criteria are discussed.

Author: D.F. Griffiths
Publisher: CRC Press
ISBN: 1000158055
Category : Mathematics
Languages : en
Pages : 293

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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.

Author: Daniel P. Palomar
Publisher: Cambridge University Press
ISBN: 0521762227
Category : Computers
Languages : en
Pages : 513

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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: Gianni Pillo
Publisher: Springer Science & Business Media
ISBN: 1475732260
Category : Mathematics
Languages : en
Pages : 484

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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: M.S. Moonen
Publisher: Springer Science & Business Media
ISBN: 9401581967
Category : Mathematics
Languages : en
Pages : 434

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Proceedings of the NATO Advanced Study Institute, Leuven, Belgium, August 3-14, 1992