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In this paper, the mathematical programs with vanishing constraints or MPVCare considered. We prove that an MPVC-tailored penalty function, introduced in[5], is still exact under a very weak and new constraint qualification. Mostimportantly, this constraint qualification is shown to be strictly strongerthan MPVC-Abadie constraint qualification.

On an Exact Penalty Result and New Constraint Qualifications for Mathematical Programs with Vanishing Constraints