An optimal control problem with piecewise quadratic cost functional containing a ‘dead‐zone’

Abstract In this paper, we describe an exact solution method for the problem of optimally controlling a deterministic discrete linear system with piecewise quadratic cost functional containing a ‘dead‐zone’. This model generalizes the well‐known optimal control model for a linear system with (symmetric) quadratic objective functional. This more general problem is solved by using concepts and techniques from the theory of nonlinear programming, for example Kuhn‐Tucker theory, duality, linear complementarity, and Lemke's algorithm. We apply the results to the solution of a 25‐period deterministic pension funding problem which is modelled as a discrete‐time optimal control problem. The controls for this problem are company contributions and investment amounts, and the state is the value of the pension fund.