Brendan O'Donoghue

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

    Hamiltonian Descent Methods

  • Arnaud Doucet
  • Chris J. Maddison
  • Brendan O'Donoghue
  • Daniel Paulin
  • Yee Whye Teh
    • Categories Convex Optimization

    We propose a family of optimization methods that achieve linear convergence using first-order gradient information and constant step sizes on a class of convex functions much larger than the smooth and strongly convex ones. This larger class includes functions whose second derivatives may be singular or unbounded at their minima. Our methods are discretizations of … Read more