Sequential Convex Programming Methods for A Class of Structured Nonlinear Programming

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.