Optimization of an Economic System Using Nonlinear Decomposition

Abstract

Abstract In this paper we consider the optimal control of a discrete-time linear-quadratic economic system with constant coefficients. The controls have upper and lower bounds, which makes a straightforward linear-quadratic Riccati equation approach impossible. By a Lagrangean relaxation of the control bound constraints, we obtain an auxiliary problem for which the standard approach can be applied. Two methods for finding the optimal Lagrange multipliers are used. The first is a simple price adjustment procedure; the second employs a nonlinear Dantzig-Wolfe type master problem. As an illustration, we solve a small numerical example. Convergence aspects of the methods are discussed, and an economic interpretation of the approach is given.