- Douglas-Rachford Algorithm for Management- and State-constrained Optimum Management Issues
Authors: Regina S. Burachik, Bethany I. Caldwell, C. Yalçın Kaya
Summary: We take into account the applying of the Douglas-Rachford (DR) algorithm to unravel linear-quadratic (LQ) management issues with field constraints on the state and management variables. We cut up the constraints of the optimum management drawback into two units: one involving the ODE with boundary circumstances, which is affine, and the opposite a field. We rewrite the LQ management issues because the minimization of the sum of two convex capabilities. We discover the proximal mappings of those capabilities which we then make use of for the projections within the DR iterations. We suggest a numerical algorithm for computing the projection onto the affine set. We current a conjecture for locating the costates and the state constraint multipliers of the optimum management drawback, which may in flip be utilized in verifying the optimality circumstances. We stock out numerical experiments with two constrained optimum management issues for example the working and the effectivity of the DR algorithm in comparison with the normal method of direct discretization.
