Relaxed constant positive linear dependence constraint qualification (RCPLD) for a system of smooth equalities and inequalities is a constraint qualification that is weaker than the usual constraint qualifications such as Mangasarian Fromovitz constraint qualification and the linear constraint qualification. Moreover RCPLD is known to induce an error bound property. In this paper we extend RCPLD to a very general feasibility system which may include Lipschitz continuous inequality constraints, complementarity constraints and abstract constraints. We show that this RCPLD for the general system is a constraint qualification for the optimality condition in terms of limiting subdifferential and limiting normal cone and it is a sufficient condition for the error bound property under the strict complementarity condition for the complementarity system and Clarke regularity conditions for the inequality constraints and the abstract constraint set. Moreover we introduce and study some sufficient conditions for RCPLD including the relaxed constant rank constraint qualification. Finally we apply our results to the bilevel program.

光滑等式和不等式系统的松弛常数正线性依赖项约束条件（RCPLD）是一种约束条件，它比通常的约束条件（例如Mangasarian Fromovitz约束条件和线性约束条件）弱。此外，已知RCPLD会引发错误绑定属性。在本文中，我们将RCPLD扩展到一个非常通用的可行性系统，其中可能包括Lipschitz连续不等式约束，互补性约束和抽象约束。我们证明，对于一般系统，该RCPLD在限制次微分和限制法线锥方面是最优性条件的约束条件，并且在互补系统和克拉克规则性条件的严格互补条件下，对于误差约束性质是充分条件不等式约束和抽象约束集。此外，我们介绍和研究了RCPLD的一些充分条件，包括宽松的恒定秩约束条件。最后，我们将结果应用于双水平计划。