Optimality conditions for sparse nonlinear programming

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 th...

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Vydáno v:	Science China. Mathematics Ročník 60; číslo 5; s. 759 - 776
Hlavní autoři:	Pan, LiLi, Xiu, NaiHua, Fan, Jun
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Beijing Science China Press 01.05.2017 Springer Nature B.V
Témata:	Applications of Mathematics Cones Decomposition Economic models Mathematics Mathematics and Statistics Nonlinear programming Sparsity 不等式约束分解特性单核苷酸多态性最优性条件稀疏性连续可微函数非线性等式非线性规划 normal cone second-order optimality condition 90C30 90C46 first-order optimality condition sparse nonlinear programming 90C26 constraint qualification
ISSN:	1674-7283, 1869-1862
On-line přístup:	Získat plný text
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Shrnutí:	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.
Bibliografie:	sparse nonlinear programming, constraint qualification, normal cone, first-order optimality con-dition, second-order optimality condition 11-5837/O1 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. ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ISSN:	1674-7283 1869-1862
DOI:	10.1007/s11425-016-9010-x