Characterization of the robust isolated calmness for a class of conic programming problems
Characterization of the robust isolated calmness for a class of conic programming problems
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一类二次曲线规划问题的稳健孤立平静的表征
DOI：
10.1137/16m1058753
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发表时间：
2017
影响因子：
3.1
通讯作者：
Zhang Liwei
中科院分区：
文献类型：
--
作者：
Ding Chao;Sun Defeng;Zhang Liwei
本文研究了一类有趣的锥规划问题（包括最常见的应用问题）在局部最优解处的Karush-Kuhn-Tucker（KKT）解映射的鲁棒孤立镇定性.在罗宾逊约束条件下，证明了KKT解映射是鲁棒孤立镇定的当且仅当严格罗宾逊约束条件和二阶充分条件都成立.这意味着，除其他外，在局部最优解的二阶充分条件是需要的KKT解决方案映射有奥宾性质。
This paper is devoted to studying the robust isolated calmness of the Karush--Kuhn--Tucker (KKT) solution mapping for a large class of interesting conic programming problems (including most commonly known ones arising from applications) at a locally optimal solution. Under the Robinson constraint qualification, we show that the KKT solution mapping is robustly isolated calm if and only if both the strict Robinson constraint qualification and the second order sufficient condition hold. This implies, among others, that at a locally optimal solution the second order sufficient condition is needed for the KKT solution mapping to have the Aubin property.