解凸二次半定规划的过滤集-正则化方法Filter-regularization Method for Solving Convex Quadratic Semidefinite Programming
李成进;
摘要(Abstract):
给出求解一种特殊凸二次半定规划的过滤集-正则化方法,并对其全局收敛性进行分析.最后还提供此算法的初步数值试验结果.
关键词(KeyWords): 凸二次半定规划;过滤集;正则化
基金项目(Foundation): 福建省自然科学基金资助项目(2009J05003)
作者(Authors): 李成进;
参考文献(References):
- [1]Todd M J.Semidefinite optimization[J].Acta Numerica,2001,10:515-560.
- [2]Vandenberghe L,Boyd S.Semidefinite programming[J].SIAM Rev,1996(38):49-95.
- [3]Higham N J.Computing the nearest correlation matrix-a problem from finance[J].IMAJ Numer Analysis,2002(22):329-343.
- [4]Qi H D,Sun D F.Quadratic convergence and numerical experiments of Newton's method for computing thenearest correlation matrix[J].SIAMJ Mat Ana App,2006(28):360-385.
- [5]Toh K C,Tutuncu R H,Todd M J.Inexact primal-dual path-following algorithms for a special class of convexquadratic SDP and related problems[J].Pacific J Optimization,2007(3):135-164.
- [6]Li C J,Sun W Y.On filter-successive linearization methods for nonlinear semidefinite programming[J].Sciencein China,2009(52):2341-2361.
- [7]Malick J,Povh J,Rendl F,et al.Regularization methods for semidefinite programming[J].SIAM J Opt,2009(20):336-356.
- [8]Wen Z,Goldfarb D,Yin W.Alternating directionaugmented lagrangian methods for semidefinite programming[EB/OL].(2009-08-10).http://www.ca am.rice.edu/wy1/paperfiles/Rice—CAAM—TR09-42.PDF.
- [9]Fletcher R,Leyffer S,Toint P L.On the global convergence of a filter-SQP algorithm[J].SIAM Journal onOptimization,2002,13:44-59.