Self-Regularity: A New Paradigm for Primal-Dual Interior-Point Algorithms by Cornelis Roos, Tamas Terlaky, Jiming Peng (Paperback, 2002)
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- DescriptionResearch on interior-point methods (IPMs) has dominated the field of mathematical programming for the last two decades. Two contrasting approaches in the analysis and implementation of IPMs are the so-called small-update and large-update methods, although, until w, there has been a torious gap between the theory and practical performance of these two strategies. This book comes close to bridging that gap, presenting a new framework for the theory of primal-dual IPMs based on the tion of the self-regularity of a function. The authors deal with linear optimization, nlinear complementarity problems, semidefinite optimization, and second-order conic optimization problems. The framework also covers large classes of linear complementarity problems and convex optimization. The algorithm considered can be interpreted as a path-following method or a potential reduction method. Starting from a primal-dual strictly feasible point, the algorithm chooses a search direction defined by some Newton-type system derived from the self-regular proximity. The iterate is then updated, with the iterates staying in a certain neighborhood of the central path until an approximate solution to the problem is found. By extensively exploring some intriguing properties of self-regular functions, the authors establish that the complexity of large-update IPMs can come arbitrarily close to the best kwn iteration bounds of IPMs. Researchers and postgraduate students in all areas of linear and nlinear optimization will find this book an important and invaluable aid to their work.
- Author BiographyJiming Peng is Professor of Mathematics at McMaster University and has published widely on nonlinear programming and interior-points methods. Cornelis Roos holds joint professorships at Delft University of Technology and Leiden University. He is an editor of several journals, coauthor of more than 100 papers, and coauthor (with Tamas Terlaky and Jean-Philippe Vial) of Theory and Algorithms for Linear Optimization . Tamas Terlaky is Professor in the Department of Computing and Software at McMaster University, founding Editor in Chief of Optimization and Engineering , coauthor of more than 100 papers, and an editor of several journals and two books.
- Author(s)Cornelis Roos,Jiming Peng,Tamas Terlaky
- PublisherPrinceton University Press
- Date of Publication07/10/2002
- Series TitlePrinceton Series in Applied Mathematics
- Place of PublicationNew Jersey
- Country of PublicationUnited States
- ImprintPrinceton University Press
- Content Note1, black & white illustrations
- Weight28 g
- Width152 mm
- Height229 mm
- Spine11 mm
- Format DetailsTrade paperback (US)
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