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dc.contributor.authorGoldstein, Allen A.
dc.date1989-02
dc.date.accessioned2013-03-07T21:52:57Z
dc.date.available2013-03-07T21:52:57Z
dc.date.issued1989-02
dc.identifier.urihttp://hdl.handle.net/10945/29911
dc.descriptionApproved for public release; distribution is unlimited.en_US
dc.description.abstractPt.1. 1) Relying on a theorem of Nemerovsky and Yuden(1979) a lower bound is given for the efficiency of global Newton methods over the class C1(mu, Lambda). 2) The efficiency of Smale's global Newton method in a simple setting with a nonsingular, Lipschitz-continuous Jacobian is considered. The efficiency is characterized by 2 parameters, the condition number Q and the smoothness S. The efficiency is sensitive to S, and insensitive to Q. Keywords: Unconstrained optimization, Computational complexity, Algorithms. (JD)--Pt. 2. Newton's method applied to certain problems with a discontinuous derivative operator is shown to be effective. A global Newton method in this setting is exhibited and its computational complexity is estimated. As an application a method is proposed to solve problems of linear inequalities (linear programming, phase 1). Using an example of the Klee-Minty type due to Blair, it was found that the simplex method (used in super-lindo) required over 2,000 iterations, while the method above required an average of 8 iterations (Newton steps) over 15 random starting values. Keywords; Linear programming; Computational complexity. (JHD)en_US
dc.description.sponsorshipNaval Surface Weapons Center, Dahlgren, VAen_US
dc.description.urihttp://archive.org/details/howgoodareglobal00gold
dc.language.isoen_US
dc.publisherMonterey, California. Naval Postgraduate Schoolen_US
dc.rightsThis publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. As such, it is in the public domain, and under the provisions of Title 17, United States Code, Section 105, may not be copyrighted.en_US
dc.subject.lcshNUMERICAL METHODS AND PROCEDURESen_US
dc.titleHow good are Global Newton methods?en_US
dc.typeReporten_US
dc.contributor.corporateNaval Postgraduate School (U.S.)
dc.subject.authorLinear Programmingen_US
dc.subject.authorComputational Complexityen_US
dc.subject.authorLinear programmingen_US
dc.subject.authorComputational complexityen_US
dc.description.funderO&MN Direct Fundingen_US
dc.identifier.npsreportNPS-53-88-010


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