Journal of Guangdong University of Technology ›› 2022, Vol. 39 ›› Issue (04): 32-35,45.doi: 10.12052/gdutxb.210002

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Characterization of Contingent Tangent Cone and Limiting Norm Cone to Half Complementary Set

Jia Ling-ling, Liu Yu-lan   

  1. School of Mathematics and Statistics, Guangdong University of Technology, Guangzhou 510520, China
  • Received:2021-01-06 Online:2022-07-10 Published:2022-06-29

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Abstract: According to the variational properties of zero-norm function, the optimizations with zero-norm constraint or zero-norm regularized optimizations or zero-nom minimized problems can be reformed to the constraint optimizations with half complementary set. It is well known that the characterization of contingent tangent cone and limiting norm cone to the constraint set is crucial in proposing the optimal conditions for these optimizations. The contingent tangent cone, regular norm cone and limiting norm cone are characterized to the half complementary set. It enriches the optimality theory of discontinuous and nonconvex programming problems and gives a key theoretical basis to study further these optimization problems.

Key words: zero-norm, half complementary set, contingent tangent cone, regular norm cone, limiting norm cone

CLC Number: 

  • O224
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