LAUSR

Recently, Hoheisel et al. (Nonlinear Anal 72(5):2514–2526, 2010) proved the exactness of the classical $$l_1$$l1 penalty function for the mathematical programs with vanishing constraints (MPVC) under the MPVC-linearly independent constraint qualification (MPVC-LICQ) and the bi-active set being empty at a local minimum $$x^*$$x∗ of MPVC. In this paper, by relaxing the two conditions in the above result, we show that the $$l_1$$l1 penalty function is still exact at a local minimum $$x^*$$x∗ of MPVC under the MPVC-generalized pseudonormality and a new assumption. Our $$l_1$$l1 exact penalty result includes the one of Hoheisel et al. as a special case.