We study systems of equations, F (x) = 0, given by piecewise differentiable functions F : Rn → Rk, k ≤ n. The focus is on the representability of the solution set locally as an (n − k)-dimensional Lipschitz manifold. For that, nonsmooth versions of inverse function theorems are applied. It...

In this paper we apply two convexification procedures to the Lagrangian of a nonconvex semi-infinite programming problem. Under the reduction approach it is shown that, locally around a local minimizer, this problem can be transformed equivalently in such a way that the transformed Lagrangian...