Journal
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
Volume 175, Issue 1, Pages 104-118Publisher
SPRINGER/PLENUM PUBLISHERS
DOI: 10.1007/s10957-017-1166-4
Keywords
Cardinality constraint; Cone programming; Optimality condition; Constraint qualification
Funding
- National Natural Science Foundation of China [11431002, 11771038, 11771255]
- Shandong Province Natural Science Foundation [ZR2016AM07]
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In this paper, optimality conditions are presented and analyzed for the cardinality-constrained cone programming arising from finance, statistical regression, signal processing, etc. By introducing a restricted form of (strict) Robinson constraint qualification, the first-order optimality conditions for the cardinality-constrained cone programming are established based upon the properties of the normal cone. After characterizing further the second-order tangent set to the cardinality-constrained system, the second-order optimality conditions are also presented under some mild conditions. These proposed optimality conditions, to some extent, enrich the optimization theory for noncontinuous and nonconvex programming problems.
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