Author(s)

Qingjie Hu¹, Zhijuan Zhou², Yu Chen³

¹Guangxi Key Laboratory of Automatic Detecting Technology and Instruments, Guilin, China.
²School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin, China.
³School of Mathematics and Statistics, Guangxi Normal University, Guilin, China.

In this paper, by using the notion of convexificator, we introduce the generalized standard Abadie constraint qualification and the generalized MPVC Abadie constraint qualification, and define the generalized stationary conditions for the nonsmooth mathematical program with vanishing constraints (MPVC for short). We show that the generalized strong stationary is the first order necessary optimality condition for nonsmooth MPVC under the generalized standard Abadie constraint qualification. Sufficient conditions for global or local optimality for nonsmooth MPVC are also derived under some generalized convexity assumptions.

Mathematical Program with Vanishing Constraints, Optimality Conditions, Convexificator

Hu, Q. , Zhou, Z. and Chen, Y. (2021) Some Convexificators-Based Optimality Conditions for Nonsmooth Mathematical Program with Vanishing Constraints. American Journal of Operations Research, 11, 324-337. doi: 10.4236/ajor.2021.116020.