A Newton-Type Algorithm for the Solution of the Implicit Programming Problem

A second-order algorithm is presented for the solution of the implicit programming problem. The implicit programming problem is a mathematical programming problem that has as its solution the optimal steady-states of an optimal control problem defined on an infinite horizon. The algorithm is shown to be a variant of Newton's method for solving a fixed-point problem defined implicitly by the implicit programming problem. Local and global convergence properties of the algorithm are briefly discussed.