On duality for nonsmooth mathematical problems with vanishing constraints

In this paper, we investigate a duality theory for nonsmooth optimization problems with vanishing constraints (MPVC) defined by locally Lipschitz functions. In order to do this, we first formulate a new mixed-type dual problem for the considered MPVC, which is a generalization of Wolfe and Mond–Weir dual problems. Since this dual problem depends on the feasible points of the primal problem, we introduce another mixed-type dual problem that does not have this dependence. Then, we present the weak, strong, converse, restricted converse, and the strict converse duality results for these parametric dual problems. Finally, we compae the results of the article written by Mishra et al. (Ann Oper Res 243(1):249–272, 2016) with our results and state the correct version of some of its incorrect theorems.