半互补集合的相依切锥和极限法锥的刻画

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

根据零模函数的变分性质,带有零模约束的优化问题、零模正则问题和零模极小化问题都可以转化为带有半互补约束集合的约束优化问题。而刻画约束优化问题的约束集合的相依切锥和极限法锥,对获得该优化问题的最优性条件起着至关重要的作用。本文主要刻画了半互补集合的相依切锥、正则法锥和极限法锥,丰富了非连续、非凸规划问题的最优性理论,为进一步研究带有零模约束的优化问题、零模正则问题和零模极小化问题奠定了理论基础。

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.