conic programs

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

    Projection: A Unified Approach to Semi-Infinite Linear Programs and Duality in Convex Programming

  • Amitabh Basu
  • Kipp Martin
  • Christopher Thomas Ryan
    • Categories Convex Optimization, Linear, Cone and Semidefinite Programming, Semi-infinite Programming Tags , , , ,

    Fourier-Motzkin elimination is a projection algorithm for solving finite linear programs. We extend Fourier-Motzkin elimination to semi-infinite linear programs which are linear programs with finitely many variables and infinitely many constraints. Applying projection leads to new characterizations of important properties for primal-dual pairs of semi-infinite programs such as zero duality gap, feasibility, boundedness, and solvability. … Read more