论文标题
具有基数约束的数学程序的顺序最佳条件
A sequential optimality condition for Mathematical Programs with Cardinality Constraints
论文作者
论文摘要
在本文中，我们提出了一个近似弱的平稳性（$ aw $ stationarity）概念，旨在处理具有基数约束的{\ em数学程序}（MPCAC），我们证明了这是独立于任何约束资格的合法优化条件。这样的顺序最佳条件改善了先前工作中提出的较弱的平稳性条件。在过去的几年中，已经针对非线性约束优化解决了关于顺序最佳条件的许多研究，其中一些在MPCC的背景下进行了工作，据我们所知，尚未提出针对MPCAC问题的顺序最佳条件。我们还建立了$ aw $ stationarity和其他常规的顺序最佳条件（例如AKKT，CAKKT和PAKKT）之间的一些关系。我们指出，尽管顺序最佳条件具有计算吸引力，但在这项工作中，我们并不关心算法后果。我们的目标纯粹是讨论有关MPCAC问题的此类条件的理论方面。
In this paper we propose an Approximate Weak stationarity ($AW$-stationarity) concept designed to deal with {\em Mathematical Programs with Cardinality Constraints} (MPCaC), and we proved that it is a legitimate optimality condition independently of any constraint qualification. Such a sequential optimality condition improves weaker stationarity conditions, presented in a previous work. Many research on sequential optimality conditions has been addressed for nonlinear constrained optimization in the last few years, some works in the context of MPCC and, as far as we know, no sequential optimality condition has been proposed for MPCaC problems. We also establish some relationships between our $AW$-stationarity and other usual sequential optimality conditions, such as AKKT, CAKKT and PAKKT. We point out that, despite the computational appeal of the sequential optimality conditions, in this work we are not concerned with algorithmic consequences. Our aim is purely to discuss theoretical aspects of such conditions for MPCaC problems.
