Physical Sciences and Mathematics Commons^™

A Monotone Follower Control Problem With A Nonconvex Functional And Some Related Problems, Jamiiru Luttamaguzi

LSU Doctoral Dissertations

A generalized one-dimensional monotone follower control problem with a nonconvex functional is considered. The controls are assumed to be nonnegative progressively measurable processes. The verification theorem for this problem is presented. A specific monotone follower control problem with a nonconvex functional is then considered in which the diffusion term is constant. The optimal control for this problem, which is explicitly given, can be viewed as tracking a standard Wiener process by a non anticipating process starting at 0. For some parameters values, the value function for this monotone follower control problem is shown to be C² and for other …