Critical Point Approximation Through Exact Regularization

We present several iterative methods for finding the critical points and/or the minima of a functional which is essentially the difference between two convex functions. The underlying idea relies upon partial and exact regularization of the functional, which allows us to preserve the local feature in a large number of applications, as well as to obtain some convergence results. These methods are further applied to some differential problems of the semilincar elliptic type arising in plasma physics and fluid mechanics.