论文标题
使用切换约束的数学程序的最佳条件和确切的惩罚
Optimality Conditions and Exact Penalty for Mathematical Programs with Switching Constraints
论文作者
论文摘要
在本文中，我们概述了使用切换约束（MPSC）对数学程序的确切惩罚。 MPSC是一种新的优化问题，具有一些重要的应用程序。众所周知，如果将MPSC视为标准的非线性程序，那么某些通常的约束资格可能会失败，并且无法处理这个问题，人们可以将其重新将其重新定为具有析取约束（MPDC）的数学程序。在本文中，我们首先调查了MPDC的约束资格和最佳条件的最新结果，然后将其应用于MPSC以获得相应的约束资格和最佳条件。此外，我们为MPSC的局部误差绑定和确切的惩罚结果提供两种类型的条件。一种来自MPDC的定向准正常，另一个是通过使用局部分解方法获得的。
In this paper, we give an overview on optimality conditions and exact penalization for the mathematical program with switching constraints (MPSC). MPSC is a new class of optimization problems which has some important applications. It is well-known that if MPSC is treated as a standard nonlinear program, some of the usual constraint qualifications may fail and to deal with this issue one could reformulate it as a mathematical program with disjunctive constraints (MPDC). In this paper we first survey recent results on constraint qualifications and optimality conditions for MPDC and then apply them to MPSC to obtain the corresponding constraint qualifications and optimality conditions. Moreover we provide two types of sufficient conditions for the local error bound and exact penalty results for MPSC. One comes from the directional quasi-normality for MPDC and the other is obtained by using the local decomposition approach.
