  In this paper, we consider the problem of solving a constrained system of
nonlinear equations. We propose an algorithm based on a combination of the
Newton and conditional gradient methods, and establish its local convergence
analysis. Our analysis is set up by using a majorant condition technique,
allowing us to prove in a unified way convergence results for two large
families of nonlinear functions. The first one includes functions whose
derivative satisfies a Holder-like condition, and the second one consists of a
substantial subclass of analytic functions. Numerical experiments illustrating
the applicability of the proposed method are presented, and comparisons with
some other methods are discussed.
