Christian Füllner

A new framework to generate Lagrangian cuts in multistage stochastic mixed-integer programming

  • Christian Füllner
  • Xu Andy Sun
  • Steffen Rebennack
    • Categories (Mixed) Integer Linear Programming, Stochastic Programming Tags , , , , ,

    Based on recent advances in Benders decomposition and two-stage stochastic integer programming we present a new generalized framework to generate Lagrangian cuts in multistage stochastic mixed-integer linear programming (MS-MILP). This framework can be incorporated into decomposition methods for MS-MILPs, such as the stochastic dual dynamic integer programming (SDDiP) algorithm. We show how different normalization techniques … Read more

    On Lipschitz regularization and Lagrangian cuts in multistage stochastic mixed-integer linear programming

  • Christian Füllner
  • Xu Andy Sun
  • Steffen Rebennack
    • Categories (Mixed) Integer Linear Programming, Stochastic Programming Tags , , , , ,

    We provide new theoretical insight on the generation of linear and non-convex cuts for value functions of multistage stochastic mixed-integer programs based on Lagrangian duality. First, we analyze in detail the impact that the introduction of copy constraints, and especially, the choice of the accompanying constraint set for the copy variable have on the properties … Read more

    Stochastic dual dynamic programming and its variants – a review

  • Christian Füllner
  • Steffen Rebennack
    • Categories Stochastic Programming Tags , , , , , , ,

    We provide a tutorial-type review on stochastic dual dynamic programming (SDDP), as one of the state-of-the-art solution methods for large-scale multistage stochastic programs. Since introduced about 30 years ago for solving large-scale multistage stochastic linear programming problems in energy planning, SDDP has been applied to practical problems from several fields and is enriched by various … Read more

    Deterministic upper bounds in global minimization with nonlinear equality constraints

  • Christian Füllner
  • Peter Kirst
  • Oliver Stein
    • Categories Constrained Nonlinear Optimization, Global Optimization Theory

    We address the problem of deterministically determining upper bounds in continuous non-convex global minimization of box-constrained problems with equality constraints. These upper bounds are important for the termination of spatial branch-and-bound algorithms. Our method is based on the theorem of Miranda which helps to ensure the existence of feasible points in certain boxes. Then, the … Read more