Differential Dynamic Programming for Solving Nonlinear Programming Problems

Dynamic programming is one of the methods which utilize special structures of large-scale mathematical programming problems. Conventional dynamic programming, however, can hardly solve mathematical programming problems with many constraints. This paper proposes differential dynamic programming algorithms for solving largescale nonlinear programming problems with many constraints and proves their local convergence. The present algorithms, based upon Kuhn-Tucker conditions for subproblems decomposed by dynamic programming, are composed of iterative methods for solving systems of nonlinear equations. It is shown that the convergence of the present algorithms with Newton's method is R-quadratic. Three numerical examples including the Rosen-Suzuki test problem show the efficiency of the present algorithms.