Constraint qualifications and optimality conditions for optimization problems with cardinality constraints

被引：39

作者：

Cervinka, Michal ^{[1
,2
]}

Kanzow, Christian ^{[3
]}

Schwartz, Alexandra ^{[4
]}

机构：

[1] Czech Acad Sci, Inst Informat Theory & Automat, Vodarenskou Vezi 4, Prague 18208, Czech Republic

[2] Charles Univ Prague, Inst Econ Studies, Fac Social Sci, Opletalova 26, Prague 11000, Czech Republic

[3] Univ Wurzburg, Inst Math, Emil Fischer Str 30, D-97074 Wurzburg, Germany

[4] Tech Univ Darmstadt, Grad Sch Computat Engn, Dolivostr 15, D-64293 Darmstadt, Germany

来源：

MATHEMATICAL PROGRAMMING | 2016年 / 160卷 / 1-2期

关键词：

Cardinality constraints; Constraint qualifications; Optimality conditions; KKT conditions; Strongly stationary points; LINEAR-DEPENDENCE CONDITION; MATHEMATICAL PROGRAMS; STATIONARITY;

D O I：

10.1007/s10107-016-0986-6

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

This paper considers optimization problems with cardinality constraints. Based on a recently introduced reformulation of this problem as a nonlinear program with continuous variables, we first define some problem-tailored constraint qualifications and then show how these constraint qualifications can be used to obtain suitable optimality conditions for cardinality constrained problems. Here, the (KKT-like) optimality conditions hold under much weaker assumptions than the corresponding result that is known for the somewhat related class of mathematical programs with complementarity constraints.

引用

页码：353 / 377

页数：25

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