MARC record from Internet Archive

LEADER: 02693nam 2200385 a 45 0
001 a199448
008 980625m19881989caua b f000|0 eng d
040 $aCMontNP$cCMontNP
086 0 $aD 208.14/2:NPS-53-88-010
086 0 $aD 208.14/2:NPS-53-89-010
100 1 $aGoldstein, Allen A.
245 10 $aHow good are Global Newton methods? /$cAllen Goldstein.
260 $aMonterey, Calif. :$bNaval Postgraduate School ;$aSpringfield, Va. :$bAvailable from National Technical Information Service,$c[1988-1989]
300 $a2 v. ;$c28 cm.
500 $aTitle from cover.
500 $a"NPS-53-89-010."--part I.
500 $a"NPS-53-88-010."--part II.
500 $a"February 1989."--part I.
500 $a"September 1988."--part II.
500 $aAD A208 390--pat I.
500 $aAD A201 099--part II.
504 $aIncludes bibliographical references.
520 $aPt.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)
592 $aaq/aq cc:9116 06/25/98
650 4 $aNUMERICAL METHODS AND PROCEDURES.
650 4 $aINEQUALITIES.
650 4 $aLINEAR PROGRAMMING.
650 4 $aITERATIONS.
710 2 $aNaval Postgraduate School (U.S.).$bDept. of Mathematics.
740 01 $aNPS-53-88-010.
740 01 $aNPS-53-89-010.
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926 $aNPS-LIB$bDIGIPROJ$cD 208.14/2:NPS-53-89-010$dBOOK$eNEVER$f1
926 $aNPS-LIB$bFEDDOCS$cD 208.14/2:NPS-53-89-010$dBOOK$f2