The Semi-Isolated Calmness Of The KKT System For The Parameterized Optimization Problems

In this paper,the local uniform isolation stability of KKT demapping and the semi-isolation stationary of KKT demapping are studied.Firstly,in the case that the Lagrangian multiplier is not unique,the second-order sufficient condition is proved to contain the locally consistent isolated stability of the KKT demapping at the corresponding point.In addition,by a simplified way,the characterization The KKT demapping is the transfer of locally consistent isolated stationaryness at the corresponding point.Also,in mapping DxG(x,u):X?Y Under certain restric-tions of,the non-criticality of the Lagrangian multiplier A also guarantees that the KKT demapping is locally consistent and stable.Therefore,there is sufficient fea-ture for obtaining the semi-isolational stationary of the solution mapping.Finally,the stationarity of the multi-valued function at the corresponding point is equivalent to the stationarity of the multiplier subset map at the corresponding point.It is proved that the KKT demapping is semi-isolated and stable at the corresponding point.The multiplier subset map is stable at the corresponding point.And KKT demapping is locally consistent and stationary at the corresponding points.So the semi-isolational stationary of KKT demapping has sufficient features.