The Non convexities Problem: A Simple Computational Solution

In the last few years new attention has been paid to the problem of nonconvexities in the cost-to-go function in adaptive control models. Using analytical methods, it can be found that nonconvexities are caused by the probing component of the total cost-to-go (Mizrach, 1991) or by the cautionary component of the cost-to-go (Amman and Kendrick, 1995). In this paper a simple algorithm based on the usual gradient methods, able to detect the presence of nonconvexities in an adaptive control problem and to find the global optimum, is presented and its effectiveness is studied in a Monte Carlo experiment. The simulations reported show that this code seems well suited for most of the situations likely to occur in empirical studies. In the future this algorithm must be tested in larger models to see if these results hold in more complex situations.