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-...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.展开更多
In this paper,we study optimization problems with the sparsity constraints.Firstly we give the expressions of the Mordukhovich(the limiting)normal cone of sparsity constraint and its intersection with a polyhedral set...In this paper,we study optimization problems with the sparsity constraints.Firstly we give the expressions of the Mordukhovich(the limiting)normal cone of sparsity constraint and its intersection with a polyhedral set,and then based on these expressions we present the first-order necessary conditions for sparsity constrained optimization.展开更多
基金supported in part by the National Natural Science Foundation of China(Nos.11431002,71271021).
文摘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.
基金supported by the National Natural Sciences Foundation of China(No.11371116)Innovation Foundation for Graduate Students of Harbin Normal University(No.HSDSSCX2015-28).
文摘In this paper,we study optimization problems with the sparsity constraints.Firstly we give the expressions of the Mordukhovich(the limiting)normal cone of sparsity constraint and its intersection with a polyhedral set,and then based on these expressions we present the first-order necessary conditions for sparsity constrained optimization.
