摘要
本文提出了一种求解半定规划的邻近外梯度算法.通过转化半定规划的最优性条件为变分不等式,在变分不等式满足单调性和Lipschitz连续的前提下,构造包含原投影区域的半空间,产生邻近点序列来逼近变分不等式的解,简化了投影的求解过程.将该算法应用到教育测评问题中,数值实验结果表明,该方法是解大规模半定规划问题的一种可行方法.
In this paper,we present a proximal extragradient algorithm for solving semidefinite programming probem.The optimality conditions for semidefinite programming are transformed into variational inequality problem.Under the premise of variational inequality monotone and Lipschitz continuous,half-space contains the original projection area is constructed,generated points sequence is approaching the solution of variational inequalities,such that the projection of the solution process is simplified.The algorithm is applied to educational evaluation questions,and numerical results show that the proposed method is feasible for solving large-scale semidefinite programming problem.
出处
《数学杂志》
CSCD
北大核心
2016年第5期1047-1055,共9页
Journal of Mathematics
基金
教育部高校博士学科科研基金联合资助项目(20132121110009)
国家自然科学基金天元基金(11326224)
辽宁省教育厅基金资助项目(L2012105)
关键词
半定规划
变分不等式
次梯度半空间
外梯度算法
semidefinite programming（SDP）
variational inequalities
subgradient half space
extragradient algorithm
