A new use of Douglas–Rachford splitting for identifying infeasible, unbounded, and pathological conic programs

  • Yanli Liu
  • Ernest K. Ryu
  • Wotao YinEmail author
Full Length Paper Series A


In this paper, we present a method for identifying infeasible, unbounded, and pathological conic programs based on Douglas–Rachford splitting. 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.


Douglas–Rachford splitting Infeasible Unbounded Pathological Conic programs 

Mathematics Subject Classification

47H05 65K05 65K15 90C25 



W. Yin would like to thank Professor Yinyu Ye for his question regarding ADMM applied to infeasible linear programs during the 2014 Workshop on Optimization for Modern Computation held at Peking University.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature and Mathematical Optimization Society 2018

Authors and Affiliations

  1. 1.Department of MathematicsUCLALos AngelesUSA

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