  In this paper we study a broad class of structured nonlinear programming
(SNLP) problems. In particular, we first establish the first-order optimality
conditions for them. Then we propose sequential convex programming (SCP)
methods for solving them in which each iteration is obtained by solving a
convex programming problem. Under some suitable assumptions, we establish that
any accumulation point of the sequence generated by the methods is a KKT point
of the SNLP problems. In addition, we propose a variant of the SCP method for
SNLP in which nonmonotone scheme and ``local'' Lipschitz constants of the
associated functions are used. A similar convergence result as mentioned above
is established.
