Jeffrey Christiansen

A parallelizable augmented Lagrangian method applied to large-scale non-convex-constrained optimization problems

  • Natashia Boland
  • Brian Dandurand
  • Andrew C. Eberhard
  • Fabricio Oliveira
  • Jeffrey Christiansen
    • Categories (Mixed) Integer Nonlinear Programming, Constrained Nonlinear Optimization, Parallel Algorithms Tags , , , ,

    We contribute improvements to a Lagrangian dual solution approach applied to large-scale optimization problems whose objective functions are convex, continuously differentiable and possibly nonlinear, while the non-relaxed constraint set is compact but not necessarily convex. Such problems arise, for example, in the split-variable deterministic reformulation of stochastic mixed-integer optimization problems. The dual solution approach needs … Read more

    Combining Penalty-based and Gauss-Seidel Methods for solving Stochastic Mixed-Integer Problems

  • Eberhard Andrew
  • Brian Dandurand
  • Fabricio Oliveira
  • Jeffrey Christiansen
    • Categories Stochastic Programming Tags , , , ,

    In this paper, we propose a novel decomposition approach for mixed-integer stochastic programming (SMIP) problems that is inspired by the combination of penalty-based Lagrangian and block Gauss-Seidel methods (PBGS). In this sense, PBGS is developed such that the inherent decomposable structure that SMIPs present can be exploited in a computationally efficient manner. The performance of … Read more

    Combining Progressive Hedging with a Frank-Wolfe Method to Compute Lagrangian Dual Bounds in Stochastic Mixed-Integer Programming

  • Natashia Boland
  • Brian Dandurand
  • Andrew C. Eberhard
  • Jeff Linderoth
  • James R. Luedtke
  • Fabricio Oliveira
  • Jeffrey Christiansen
    • Categories (Mixed) Integer Linear Programming, Stochastic Programming Tags , , ,

    We present a new primal-dual algorithm for computing the value of the Lagrangian dual of a stochastic mixed-integer program (SMIP) formed by relaxing its nonanticipativity constraints. The algorithm relies on the well-known progressive hedging method, but unlike previous progressive hedging approaches for SMIP, our algorithm can be shown to converge to the optimal Lagrangian dual … Read more