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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Bibliographic Details
Published inScience China. Mathematics Vol. 60; no. 5; pp. 759 - 776
Main Authors Pan, LiLi, Xiu, NaiHua, Fan, Jun
Format Journal Article
LanguageEnglish
Published Beijing Science China Press 01.05.2017
Springer Nature B.V
Subjects
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
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ISSN1674-7283
1869-1862
DOI10.1007/s11425-016-9010-x

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Summary: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.
Bibliography: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.
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ISSN:1674-7283
1869-1862
DOI:10.1007/s11425-016-9010-x