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

Sequential Convex Programming Methods for A Class of Structured Nonlinear Programming