Primal-Dual Interior-Point Methods for Second-Order
Conic Optimization Based on Self-Regular Proximities
Based on the notion of self-regularity associated with the second-order cone, this chapter deals with primal-dual Newton methods for solving SOCO problems. After a brief introduction to the problem under consideration, general analytical functions associated with the second-order cone are introduced and versatile properties of these functions are exploited. Special attention is paid to self-regular functions and self-regular proximities related to the second-order cone K. New search directions for large-update primal-dual IPMsfor solving the underlying problem are then proposed and the complexity results of the corresponding algorithms are presented.
Questia, a part of Gale, Cengage Learning. www.questia.com
Publication information: Book title: Self-Regularity:A New Paradigm for Primal-Dual Interior-Point Algorithms. Contributors: Jiming Peng - Author, Cornelis Roos - Author, Tamás Terlaky - Author. Publisher: Princeton University Press. Place of publication: Princeton, NJ. Publication year: 2002. Page number: 125.
This material is protected by copyright and, with the exception of fair use, may not be further copied, distributed or transmitted in any form or by any means.