Optimality Conditions for Nonconvex Constrained Optimization Problems

被引：9

作者：

Mashkoorzadeh, F. ^{[1
]}

Movahedian, N. ^{[1
]}

Nobakhtian, S. ^{[1
,2
]}

机构：

[1] Univ Isfahan, Dept Math, Esfahan, Iran

[2] Inst Res Fundamental Sci IPM, POB 19395-5746, Tehran, Iran

来源：

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION | 2019年 / 40卷 / 16期

关键词：

Constraint qualification; nonconvex optimization; nonsmooth optimization; optimality condition; tangential subdifferential; QUALIFICATION;

D O I：

10.1080/01630563.2019.1640249

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present optimality conditions for a class of nonsmooth and nonconvex constrained optimization problems. To achieve this aim, various well-known constraint qualifications are extended based on the concept of tangential subdifferential and the relations between them are investigated. Moreover, local and global necessary and sufficient optimality conditions are derived in the absence of convexity of the feasible set. In addition to the theoretical results, several examples are provided to illustrate the advantage of our outcomes.

引用

页码：1918 / 1938

页数：21

共 21 条

[11]

GIORGI G, 2013, ANN U BUCHAR, V4, P479

[12] Necessary and sufficient KKT optimality conditions in non-convex optimization [J].

Ho, Quyen .

OPTIMIZATION LETTERS, 2017, 11 (01) :41-46

[13] On representations of the feasible set in convex optimization [J].

Lasserre, Jean Bernard .

OPTIMIZATION LETTERS, 2010, 4 (01) :1-5

[14]

Lemarechal C., 1986, Optimization, V17, P827, DOI 10.1080/02331938608843204

[15]

LEWIS A.S., 2010, Convex Analysis and Nonlinear Optimization: Theory and Examples

[16] Abadie's constraint qualification, metric regularity, and error bounds for differentiable convex inequalities [J].

Li, W .

SIAM JOURNAL ON OPTIMIZATION, 1997, 7 (04) :966-978

[17]

Long XJ, 2016, J NONLINEAR CONVEX A, V17, P251

[18] Optimality Conditions of Approximate Solutions for Nonsmooth Semi-infinite Programming Problems [J].

Long X.-J. ;

Xiao Y.-B. ;

Huang N.-J. .

Journal of the Operations Research Society of China, 2018, 6 (02) :289-299

[19] CONSTRAINT QUALIFICATIONS IN MULTIOBJECTIVE OPTIMIZATION PROBLEMS - DIFFERENTIABLE CASE [J].

MAEDA, T .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 1994, 80 (03) :483-500

[20] On constraint qualification in multiobjective optimization problems: Semidifferentiable case [J].

Preda, V ;

Chitescu, I .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 1999, 100 (02) :417-433

← 1 2 3 →