A New Use of Douglas-Rachford Splitting and ADMM for Identifying Infeasible, Unbounded, and Pathological Conic Programs
Yanli Liu (yanlimath.ucla.edu)
Abstract: 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. Asa first-order method, the proposed algorithm relies on simple subroutines, and therefore is simple to implement and has low per-iteration cost.
Keywords: Douglas-Rachford Splitting, infeasible, unbounded, pathological, conic programs
Category 1: Linear, Cone and Semidefinite Programming
Category 2: Convex and Nonsmooth Optimization
Category 3: Nonlinear Optimization
Citation: Liu, Yanli, Ernest K. Ryu, and Wotao Yin. "A New Use of Douglas-Rachford Splitting and ADMM for Identifying Infeasible, Unbounded, and Pathological Conic Programs." arXiv preprint arXiv:1706.02374 (2017).
Entry Submitted: 05/24/2017
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