The Vu-Decomposition Algorithm For Semi-infinite Programming

The vu-decomposition algorithm was proposed for non-smooth functions with a smooth sub-structure by Lemarechal, Mifflin, Sagastizabal and Oustry. Now we have this method applied to the semi-infinite programming. We focus the nonsmooth characteristics on the V-space, with an intermediate function, the u-Lagrangian functions, then we can extend the function on a smooth track which is tangential with the U space, and design algorithms and prove its convergence. This algorithm is super-linear convergence, because in the vu-decomposition algorithm, it includes the u-step and V-step, while the u-step is actually a Newton-step, which ensures that the design of the algorithm is super-linear.Then in this paper we will give the optimization condition, and try to use the exe-cutable algorithm to give a numerical example, and verify the validity of the method.