计算机科学 ›› 2017, Vol. 44 ›› Issue (7): 267-269.doi: 10.11896/j.issn.1002-137X.2017.07.047
陈小彪,李耿华,梁娟,王建军
CHEN Xiao-biao, LI Geng-hua, LIANG Juan and WANG Jian-jun
摘要： 近来,交替方向法成为了学者们研究的热点。对于一类子问题能够精确求解的变分不等式,该算法是有效的。然而,在实际问题中,变分不等式的子问题是非常困难甚至是不可能精确求解的。在渐近点算法的基础上得到一种非精确的渐近点算法,使得变分不等式子问题具有显式解,通过简单的预测校正步得到子问题的解。在合理的假设下,算法的收敛性得到了证明,一些数值实验表明了所提算法的有效性。
| [1] BOYD S,PARIKH N,CHU E,et al.Distributed optimizationand statistical learning via the alternating direction method of multipliers[J].Foun Trends Mach Learn,2011,3(1):1-122. [2] NAGURNEY A,ZHANG D.Projected Dynamical System and Variatioal Inequalities with Applications[M].Kluwer Acade-mic,Boston,1996. [3] FUKUSHIMA M.Application of the alternating directions me-thod of multipliers to separable convex programming problems[J].Computational Optimization and Applications,1992,1(1):93-111. [4] GLOWINSKI R,MARROCCO A.Sur l’approximation par élé-ments finisd’ ordre un et la résolution par pénalisation-dualité d’une classe de problémes de Dirichlet non linéaires[J].Journal of Equine Veterinary Science,1975,31(5):41-76. [5] ECKSTEIN J,BERTSEKAS D P.On the Douglas-Rachford split-ting method and the proximal point algorithm for maximal mono-tone operators[J].Mathematical Programming,1992,55:293-318. [6] HE B S,LIAO L Z,HAN D R,et al.A new inexact alternating directions method for monotone variational inequalities[J].Mathematical Programming,2002,2(1):103-118. [7] YE C H,YUAN X M.A descent method for structured mono-tone variational inequalities[J].Optimization Methods Software,2007,22(2):329-338. [8] HE B S,TAO M,YUAN X M.Alternating direction me-thod with Gaussian back substitution for Separable convex programming[J].SIAM J.Optimization,2012,2(2):313-340. [9] HE B S.Parallel splitting augmented Lagrangian methods formonotone structured variational inequalities Computational[J].Optimization and Applications,2009,42(2):195-212. [10] CAI X J,GU G Y,HE B S,et al.A proximal point algorithmrevisit on the alternating direction method of multipliers[J].Science China Mathematics,2013,56(10):2179-2186. [11] TAO M,YUAN X M.An inexact parallel splitting augmented Lagrangian method for monotone variational inequalities with separable structures[J].Computational Optimization and Applications,2012,52(2):439-461. [12] HE B S,LIAO L Z,YUAN X M.Alternating projection based prediction-correction methods for structured variational inequalities[J].Computational Mathematics,2006,4(6):693-710. [13] CHEN Z M,WAN L,YANG Q Z.An Inexact Direction Method for Structured Variational Inequalities[J].Journal of Optimization Theory & Applications,2014,3(2):439-459. [14] GU G Y,HE B S,YANG J F.Inexact Alternating Direction-Based Contraction Methods for Separable Linearly Constrained Convex Optimization[J].Journal of Optimization Theory and Applications,2013,163(1):105-129. |
| No related articles found! |
|
||
首页