On Solutions of Sparsity Constrained Optimizatio  

作　　者：Li-Li Pan Nai-Hua Xiu Sheng-Long Zhou 

机构地区：[1]Department of Applied Mathematics,Beijing Jiaotong University,Beijing 100044,China [2]Department of Mathematics,Shandong University of Technology,Zibo 255049,Shandong,China [3]School of Mathematics,University of Southampton,Southampton SO171BJ,UK

出　　处：《Journal of the Operations Research Society of China》2015年第4期421-439,共19页中国运筹学会会刊（英文）

基　　金：supported in part by the National Natural Science Foundation of China(Nos.11431002,71271021).

摘　　要：In this paper,we mainly study the existence of solutions to sparsity constrained optimization(SCO).Based on the expressions of tangent cone and normal cone of sparsity constraint,we present and characterize two first-order necessary optimality conditions for SCO:N-stationarity and T-stationarity.Then we give the second-order necessary and sufficient optimality conditions for SCO.At last,we extend these results to SCO with nonnegative constraint.

关 键 词：Sparsity constrained optimization Tangent cone Normal cone First-order optimality condition Second-order optimality condition 

分 类 号：O17[理学—数学]