Mathematical Programs with Semidefinite Cone Complementarity Constraints: Constraint Qualifications and Optimality Conditions

2013 ◽  
Vol 22 (1) ◽  
pp. 155-187 ◽  
Author(s):  
Jia Wu ◽  
Liwei Zhang ◽  
Yi Zhang
Mathematics ◽  
2021 ◽  
Vol 9 (22) ◽  
pp. 2915
Author(s):  
Jinman Lv ◽  
Zhenhua Peng ◽  
Zhongping Wan

In this paper, we consider a class of mathematical programs with switching constraints (MPSCs) where the objective involves a non-Lipschitz term. Due to the non-Lipschitz continuity of the objective function, the existing constraint qualifications for local Lipschitz MPSCs are invalid to ensure that necessary conditions hold at the local minimizer. Therefore, we propose some MPSC-tailored qualifications which are related to the constraints and the non-Lipschitz term to ensure that local minimizers satisfy the necessary optimality conditions. Moreover, we study the weak, Mordukhovich, Bouligand, strongly (W-, M-, B-, S-) stationay, analyze what qualifications making local minimizers satisfy the (M-, B-, S-) stationay, and discuss the relationship between the given MPSC-tailored qualifications. Finally, an approximation method for solving the non-Lipschitz MPSCs is given, and we show that the accumulation point of the sequence generated by the approximation method satisfies S-stationary under the second-order necessary condition and MPSC Mangasarian-Fromovitz (MF) qualification.


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