摘要
针对KS张量互补问题,本文研究了该问题的稀疏解.由于l_(0)范数的非凸性和非连续性,求解KS张量互补问题的稀疏解是一个NP难问题.为了解决这一问题,我们将其转化为一个带约束的多项式优化问题,然后用序列二次规划(SQP)算法求解转化的问题.数值结果表明,该算法能有效地求解KS张量互补问题的稀疏解.
In view of the Ks-tensor complementarity problem,the sparse solution of this problem is studied.Due to the nonconvexity and noncontinuity of the lo-norm,it is an NP hard problem to find the sparse solution of the KS-tensor complementarity problem.In order to solve this problem,we transform it into a polynomial programming problem with constraints.Then we use the sequential quadratic programming(SQP)algorithm to solve this transformed problem.Numerical results show that the SQP algorithm can find the sparse solutions of the KS-tensor complementarity problem effectively.
作者
孙晶晶
杜守强
陈元媛
魏益民
SUN Jingjing;DU Shouqiang;CHEN Yuanyuan;WEI Yimin(School of Mathematics and Statistics,Qingdao University,Qingdao,Shandong,266071,P.R.China;School of Mathematical Science and Shanghai Key Laboratory of Contemporary Applied Mathematics,Fudan University,Shanghai,200433,P.R.China)
出处
《数学进展》
CSCD
北大核心
2023年第2期257-272,共16页
Advances in Mathematics（China）
基金
Supported by NSFC(Nos.12271108,12226413)
Nature Science Foundation of Shandong Province(No.ZR2022MA001)
Innovation Program of Shanghai Municipal Education Commission。
关键词
KS张量
张量互补问题
稀疏解
SQP算法
KS-tensor
tensor complementarity problem
sparse solution
SQP algorithm
