Oliver Hinder

Practical Large-Scale Linear Programming using Primal-Dual Hybrid Gradient

  • David Applegate
  • Mateo Díaz
  • Haihao Lu
  • Miles Lubin
  • Oliver Hinder
  • Brendan O'Donoghue
  • Warren Schudy
    • Categories Convex Optimization, Linear Programming Tags , , ,

    We present PDLP, a practical first-order method for linear programming (LP) that can solve to the high levels of accuracy that are expected in traditional LP applications. In addition, it can scale to very large problems because its core operation is matrix-vector multiplications. PDLP is derived by applying the primal-dual hybrid gradient (PDHG) method, popularized … Read more

    On the behavior of Lagrange multipliers in convex and non-convex infeasible interior point methods

  • Gabriel Haeser
  • Yinyu Ye
  • Oliver Hinder
    • Categories Nonlinear Optimization Tags , , , ,

    This paper analyzes sequences generated by infeasible interior point methods. In convex and non-convex settings, we prove that moving the primal feasibility at the same rate as complementarity will ensure that the Lagrange multiplier sequence will remain bounded, provided the limit point of the primal sequence has a Lagrange multiplier, without constraint qualification assumptions. We … Read more