- Douglas-Rachford Algorithm for Administration- and State-constrained Optimum Administration Points
Authors: Regina S. Burachik, Bethany I. Caldwell, C. Yalçın Kaya
Abstract: We ponder the making use of of the Douglas-Rachford (DR) algorithm to unravel linear-quadratic (LQ) administration points with discipline constraints on the state and administration variables. We minimize up the constraints of the optimum administration downside into two models: one involving the ODE with boundary circumstances, which is affine, and the alternative a discipline. We rewrite the LQ administration points as a result of the minimization of the sum of two convex options. We uncover the proximal mappings of these options which we then make use of for the projections inside the DR iterations. We propose a numerical algorithm for computing the projection onto the affine set. We present a conjecture for finding the costates and the state constraint multipliers of the optimum administration downside, which can in flip be utilized in verifying the optimality circumstances. We provide out numerical experiments with two constrained optimum administration points as an example the working and the effectivity of the DR algorithm compared with the usual methodology of direct discretization.
