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A New Use of Douglas-Rachford Splitting and ADMM for Identifying Infeasible, Unbounded, and Pathological Conic Programs
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In this paper, we present a method for identifying infeasible, unbounded, and pathological conic programs based on Douglas-Rachford splitting, or equivalently ADMM. When an optimization program is infeasible, unbounded, or pathological, the iterates of Douglas-Rachford splitting diverge. Somewhat surprisingly, such divergent iterates still provide useful information, which our method uses for identification. In addition, for strongly infeasible problems the method produces a separating hyperplane and informs the user on how to minimally modify the given problem to achieve strong feasibility. As a first-order method, the proposed algorithm relies on simple subroutines, and therefore is simple to implement and has low per-iteration cost.
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Operator Splitting for Convex Constrained Markov Decision Processes
OS-CMDP uses Douglas-Rachford splitting to solve convex-constrained MDPs by alternating between a quadratically regularized MDP update and a projection onto the constraint set, with convergence and infeasibility-detec...
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