NONCONVEXITIES IN STOCHASTIC-CONTROL MODELS

Nonconvexities in the criterion function of adaptive control problems were first found about ten years ago with numerical methods. Recently they have been confirmed by Mizrach with analytical methods. He found that a source of the nonconvexity was the probing component of the cost-to-go. Mizrach's results have been extended in this paper. First, the probing function has been characterized and found to support the use of algorithms which exploit this character to find the global optimum. Secondly, a new source of nonconvexities has been found in the cautionary component of the cost-to-go.