Self-Regularity

A New Paradigm for Primal-Dual Interior-Point Algorithms

Nonfiction, Science & Nature, Mathematics, Applied, Technology
Cover of the book Self-Regularity by Jiming Peng, Cornelis Roos, Tamás Terlaky, Princeton University Press
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Jiming Peng, Cornelis Roos, Tamás Terlaky ISBN: 9781400825134
Publisher: Princeton University Press Publication: January 10, 2009
Imprint: Princeton University Press Language: English
Author: Jiming Peng, Cornelis Roos, Tamás Terlaky
ISBN: 9781400825134
Publisher: Princeton University Press
Publication: January 10, 2009
Imprint: Princeton University Press
Language: English

Research 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 now, there has been a notorious 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 notion of the self-regularity of a function.

The authors deal with linear optimization, nonlinear 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 known iteration bounds of IPMs.

Researchers and postgraduate students in all areas of linear and nonlinear optimization will find this book an important and invaluable aid to their work.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

Research 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 now, there has been a notorious 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 notion of the self-regularity of a function.

The authors deal with linear optimization, nonlinear 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 known iteration bounds of IPMs.

Researchers and postgraduate students in all areas of linear and nonlinear optimization will find this book an important and invaluable aid to their work.

More books from Princeton University Press

Cover of the book Mathletics by Jiming Peng, Cornelis Roos, Tamás Terlaky
Cover of the book Degenerate Diffusion Operators Arising in Population Biology (AM-185) by Jiming Peng, Cornelis Roos, Tamás Terlaky
Cover of the book Arendt and Heidegger by Jiming Peng, Cornelis Roos, Tamás Terlaky
Cover of the book Computational Economics by Jiming Peng, Cornelis Roos, Tamás Terlaky
Cover of the book Philanthropy in America by Jiming Peng, Cornelis Roos, Tamás Terlaky
Cover of the book Why Not Kill Them All?: The Logic and Prevention of Mass Political Murder by Jiming Peng, Cornelis Roos, Tamás Terlaky
Cover of the book The Machiavellian Moment by Jiming Peng, Cornelis Roos, Tamás Terlaky
Cover of the book The Age of the Crisis of Man by Jiming Peng, Cornelis Roos, Tamás Terlaky
Cover of the book The Essential Goethe by Jiming Peng, Cornelis Roos, Tamás Terlaky
Cover of the book Success through Failure by Jiming Peng, Cornelis Roos, Tamás Terlaky
Cover of the book The Secular City by Jiming Peng, Cornelis Roos, Tamás Terlaky
Cover of the book The Concept of Presocratic Philosophy by Jiming Peng, Cornelis Roos, Tamás Terlaky
Cover of the book A Mathematical Nature Walk by Jiming Peng, Cornelis Roos, Tamás Terlaky
Cover of the book Monetary Policy, Inflation, and the Business Cycle by Jiming Peng, Cornelis Roos, Tamás Terlaky
Cover of the book The Social Origins of Language by Jiming Peng, Cornelis Roos, Tamás Terlaky
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy