[1]李成进,孙文瑜.针对非线性半定规划的一类非光滑牛顿型方法(英文)[J].南京师大学报(自然科学版),2008,31(02):1-7.
　Li Chengjin,Sun Wenyu.A Nonsmooth Newton-Type Method for Nonlinear Semidefinite Programming[J].Journal of Nanjing Normal University(Natural Science Edition),2008,31(02):1-7.
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针对非线性半定规划的一类非光滑牛顿型方法(英文)()
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《南京师大学报（自然科学版）》[ISSN:1001-4616/CN:32-1239/N]

卷:
第31卷
期数:
2008年02期
页码:
1-7
栏目:
数学
出版日期:
2008-06-30

文章信息/Info

Title:
A Nonsmooth Newton-Type Method for Nonlinear Semidefinite Programming
作者:
李成进;孙文瑜;
南京师范大学数学与计算机科学学院, 江苏南京210097
Author(s):
Li Chengjin; Sun Wenyu
School of Mathematics and Computer Science, Nanjing Normal University, Nanjing 210097, China
关键词:
非线性半定规划;  非光滑牛顿型方法;  k-张量;  收敛性
Keywords:
non linear sem ide finite prog ramm ing;  nonsmoo th New ton- typem e thod;  k-tensor;  conve rgence
分类号:
O221.2
摘要:
通过4-阶张量分析讨论了一类针对非线性半定规划的非光滑牛顿法.并给出了这种非光滑牛顿法的局部二次收敛性.
Abstract:
A nonsm ooth New ton sm ethod fo r non linear sem idefin ite programm ingw as d iscussed by using 4- tenso r analys is. The locally quadra tic convergence fo r this nonsm oo th New ton s m ethod w as also established

参考文献/References:

[ 1] SunW, Yuan Y. Optim ization Theory andM e thods: Nonlinear Programm ing[M ]. New York: Springer, 2006.
[ 2] W o lkow icz H, Sa ig al R, Vandenbe rghe L, et a.l H andbook o f Sem idefinite Prog ramm ing [M ]. Boston-Dordrech t-London:K luw erAcadem ic Pub lishe rs, 2000.
[ 3] Q i L, SunW, W ang Y. Num er ica l mu ltilinea r a lgebra and its applica tions[ J]. Frontiers ofM athem atics in Ch ina, 2007( 2): 501-526.
[ 4] Li C, SunW. An equ iva lent cond ition in convex sem ide finite prog ram [ J/OL]. http: / /www. paper. edu. cn /dow nloadpaper.
php? ser ia l- num ber= 200802- 167.
[ 5] Q i L. Converg ence ana lys is o f som e algorithm s for so lv ing nonsmoo th equations[ J]. M athema tics o f Ope ra tions Resea rch,1993, 18: 227-244.
[ 6] M a lick J, Sendov H S. C larke genera lized jacob ian o f the projection on to the cone o f positive sem idefin item atr ices[ J]. Set-Valued Analysis, 2006, 14: 273-293.
[ 7] Chan Z, Sun D. Constraint nondegene racy, strong regular ity and nonsingular ity in sem ide fin ite programm ing [ J]. S IAM JOpt, 2008, 19: 370-396.
[ 8] FlegelM L, K anzow C. A compar ison of three nondege racy conditions in sem ide finite prog ram s[ J/OL]. http: / /www. m athm atik. un-i wuerzburg. de /~ kanzow /paper /DegenPropP. pd.f
[ 9] Ca iX, SunW. A nonm onotone line search a lgo rithm for nonsm oothy d iscretem in im ax prob lem [ J]. Journa l o f Nan jing Normal University: Natural Science, 2003, 26( 4): 16-21.

备注/Memo

备注/Memo:
Foundation item:Supported by the National Natural Science Foundation of China(10231060,10501024);the Specialized Research Fund of Doc-toral Program of Higher Education of China(20040319003);the Natural Science Fund of Jiangsu Province(BK2006214);the Key Subject Fund of Nanjing Normal University
Corresponding autho r: L iCheng jin, doctora,l m ajored in num ericalm athem atics. E-m ail:ch engjin98298@ s ina. com
更新日期/Last Update: 2013-05-05