TITLE:
Some Convexificators-Based Optimality Conditions for Nonsmooth Mathematical Program with Vanishing Constraints
AUTHORS:
Qingjie Hu, Zhijuan Zhou, Yu Chen
KEYWORDS:
Mathematical Program with Vanishing Constraints, Optimality Conditions, Convexificator
JOURNAL NAME:
American Journal of Operations Research,
Vol.11 No.6,
November
22,
2021
ABSTRACT: 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.