Optimal control under nonconvexity: A generalized Hamiltonian approach

Abstract

This article extends the analysis of optimal control based on a generalized Hamiltonian which covers situations of nonconvexity. The approach offers several key advantages. First, by identifying a global solution to a constrained optimization problem, the generalized Hamiltonian approach solves the problem of distinguishing between a global optimum and the (possibly many) nonoptimal points satisfying the Pontryagyn principle under nonconvexity. Second, in our generalized approach, interpreting the slopes of the separating hypersurface as shadow prices of the states continues to hold. Third, we discuss how the generalized Hamiltonian approach can be used in solving dynamic optimization problems under nonconvexity.