unbounded

Adaptive discretization-based algorithms for semi-infinite programs with unbounded variables

  • Daniel Jungen
  • Hatim Djelassi
  • Alexander Mitsos
    • Categories Global Optimization Tags , ,

    The proof of convergence of adaptive discretization-based algorithms for semi-infinite programs (SIPs) usually relies on compact host sets for the upper- and lower-level variables. This assumption is violated in some applications, and we show that indeed convergence problems can arise when discretization-based algorithms are applied to SIPs with unbounded variables. To mitigate these convergence problems, … Read more

    A New Use of Douglas-Rachford Splitting and ADMM for Identifying Infeasible, Unbounded, and Pathological Conic Programs

  • Yanli Liu
  • Ernest K. Ryu
  • Wotao Yin
    • Categories Convex and Nonsmooth Optimization, Linear, Cone and Semidefinite Programming, Nonlinear Optimization Tags , , , ,

    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 … Read more