Sequential Convex Programming Methods for A Class of Structured Nonlinear Programming
This work addresses optimization challenges for researchers and practitioners in mathematical programming, but it appears incremental as it builds on existing SCP frameworks.
The paper tackles structured nonlinear programming problems by proposing sequential convex programming methods, establishing that accumulation points of the generated sequences are KKT points under suitable assumptions.
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.