论文标题
最佳条件和基数限制性优化问题的限制资格
Optimality conditions and constraint qualifications for cardinality constrained optimization problems
论文作者
论文摘要
基数约束优化问题（CCOP）是一个优化问题，其中任何可行点的非零组分的最大数量受到界限。在本文中，我们将CCOP视为具有分离子空间约束（MPDSC）的数学程序。由于子空间是凸多面体集的特殊情况，因此MPDSC是具有分离约束（MPDC）的数学程序的特殊情况。使用子空间的特殊结构，我们能够为分离的子空间集获得更精确的公式和（定向）正常锥。然后，我们使用MPDC的相应结果获得了一阶和二阶最优条件。得益于子空间的特殊结构，我们能够为MPDSC获得一些总体上不适合MPDC的结果。特别是我们表明，松弛的恒定正线性依赖性（RCPLD）是MPDSC的度量次数/误差绑定属性的足够条件，这对于MPDC通常不正确。最后，我们表明，根据本文提出的所有约束资格，对CCOP的某些确切惩罚。
The cardinality constrained optimization problem (CCOP) is an optimization problem where the maximum number of nonzero components of any feasible point is bounded. In this paper, we consider CCOP as a mathematical program with disjunctive subspaces constraints (MPDSC). Since a subspace is a special case of a convex polyhedral set, MPDSC is a special case of the mathematical program with disjunctive constraints (MPDC). Using the special structure of subspaces, we are able to obtain more precise formulas for the tangent and (directional) normal cones for the disjunctive set of subspaces. We then obtain first and second order optimality conditions by using the corresponding results from MPDC. Thanks to the special structure of the subspace, we are able to obtain some results for MPDSC that do not hold in general for MPDC. In particular we show that the relaxed constant positive linear dependence (RCPLD) is a sufficient condition for the metric subregularity/error bound property for MPDSC which is not true for MPDC in general. Finally we show that under all constraint qualifications presented in this paper, certain exact penalization holds for CCOP.
