Optimality conditions for sparse nonlinear programming  

作　　者：PAN LiLi XIU NaiHua FAN Jun 

机构地区：[1]Department of Mathematics, Beijing Jiaotong University [2]Department of Mathematics, Shandong University of Technology

出　　处：《Science China Mathematics》2017年第5期759-776,共18页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant No.11431002);Shandong Province Natural Science Foundation(Grant No.ZR2016AM07)

摘　　要：The sparse nonlinear programming （SNP） is to minimize a general continuously differentiable func- tion subject to sparsity, nonlinear equality and inequality constraints. We first define two restricted constraint qualifications and show how these constraint qualifications can be applied to obtain the decomposition properties of the Frechet, Mordukhovich and Clarke normal cones to the sparsity constrained feasible set. Based on the decomposition properties of the normal cones, we then present and analyze three classes of Karush-Kuhn- Tucker （KKT） conditions for the SNP. At last, we establish the second-order necessary optimality condition and sufficient optimality condition for the SNP.The sparse nonlinear programming(SNP) is to minimize a general continuously differentiable function subject to sparsity, nonlinear equality and inequality constraints. We first define two restricted constraint qualifications and show how these constraint qualifications can be applied to obtain the decomposition properties of the Fréchet, Mordukhovich and Clarke normal cones to the sparsity constrained feasible set. Based on the decomposition properties of the normal cones, we then present and analyze three classes of Karush-KuhnTucker(KKT) conditions for the SNP. At last, we establish the second-order necessary optimality condition and sufficient optimality condition for the SNP.

关 键 词：sparse nonlinear programming constraint qualification normal cone first-order optimality con-dition second-order optimality condition 

分 类 号：O221.2[理学—运筹学与控制论]