Constraint Splitting and Projection Methods for Optimal Control

Abstract: We consider a class of optimal control problems with constrained control variable. We split the ODE constraint and the control constraint of the problem so as to obtain two optimal control subproblems for each of which solutions can be written simply. Employing these simpler solutions as projections, we find numerical solutions to the original problem by applying four different projection-type methods: (i) Dykstra’s algorithm, (ii) the Douglas–Rachford (DR) method, (iii) the Aragón Artacho–Campoy (AAC) algorithm and (iv) the fast iterative shrinkage-thresholding algorithm (FISTA). The problem we study is posed in infinite-dimensional Hilbert spaces. Behaviour of the DR and AAC algorithms are explored via numerical experiments with respect to their parameters. An error analysis is also carried out numerically for a particular instance of the problem for each of the algorithms. This is joint work with Heinz Bauschke and Regina Burachik.

optimization and control

Audience: researchers in the topic

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