论文标题
放松恒定的正线性依赖性约束对分离程序的资格
Relaxed constant positive linear dependence constraint qualification for disjunctive programs
论文作者
论文摘要
析取系统是一个涉及分离集的系统，该集合是有限的许多多面体凸集的结合。在本文中，我们介绍了析取系统的松弛恒定正线性依赖性约束资格（RCPLD）的概念。对于一个脱节的系统，我们的概念比我们最近为更通用系统引入的概念（J.Glob。optim。2020）较弱，并且仍然是一个约束资格。为了获得分析系统绑定的局部误差，我们介绍了分段RCPLD，如果所有不等式约束函数分别为定期，则错误绑定属性所保留，并且其余约束函数平滑。然后，我们将结果专门针对正常截面程序，该程序包括具有平衡约束的数学程序（MPEC），具有消失约束的数学程序（MPVC）和具有切换约束（MPSC）的数学程序。对于MPEC，我们恢复了RCPLD的MPEC变体MPEC-RCPLD，并提出MPEC分段RCPLD以获得{错误绑定属性}。对于MPVC，我们介绍了新的约束资格MPVC-RCPLD和分段RCPLD，这也意味着局部错误绑定。对于MPSC，我们表明RCPLD和分段RCPLD重合，因此导致局部误差绑定。
The disjunctive system is a system involving a disjunctive set which is the union of finitely many polyhedral convex sets. In this paper, we introduce a notion of the relaxed constant positive linear dependence constraint qualification (RCPLD) for the disjunctive system. For a disjunctive system, our notion is weaker than the one we introduced for a more general system recently (J. Glob. Optim. 2020) and is still a constraint qualification. To obtain the local error bound for the disjunctive system, we introduce the piecewise RCPLD under which the error bound property holds if all inequality constraint functions are subdifferentially regular and the rest of the constraint functions are smooth. We then specialize our results to the ortho-disjunctive program, which includes the mathematical program with equilibrium constraints (MPEC), the mathematical program with vanishing constraints (MPVC) and the mathematical program with switching constraints (MPSC) as special cases. For MPEC, we recover MPEC-RCPLD, an MPEC variant of RCPLD and propose the MPEC piecewise RCPLD to obtain the {error bound property}. For MPVC, we introduce new constraint qualifications MPVC-RCPLD and the piecewise RCPLD, which also implies the local error bound. For MPSC, we show that both RCPLD and the piecewise RCPLD coincide and hence it leads to the local error bound.
