Jianzhe Zhen

An extension of the Reformulation-Linearization Technique to nonlinear optimization

  • Danique de Moor
  • Dick den Hertog
  • Jianzhe Zhen
    • Categories Constrained Nonlinear Optimization, Global Optimization Tags , , ,

    We introduce a novel Reformulation-Perspectification Technique (RPT) to obtain convex approximations of nonconvex continuous optimization problems. RPT consists of two steps, those are, a reformulation step and a perspectification step. The reformulation step generates redundant nonconvex constraints from pairwise multiplication of the existing constraints. The perspectification step then convexifies the nonconvex components by using perspective … Read more

    Mathematical Foundations of Robust and Distributionally Robust Optimization

  • Daniel Kuhn
  • Wolfram Wiesemann
  • Jianzhe Zhen
    • Categories Robust Optimization Tags , ,

    Robust and distributionally robust optimization are modeling paradigms for decision-making under uncertainty where the uncertain parameters are only known to reside in an uncertainty set or are governed by any probability distribution from within an ambiguity set, respectively, and a decision is sought that minimizes a cost function under the most adverse outcome of the … Read more

    Robust Convex Optimization: A New Perspective That Unifies And Extends

  • Dimitris Bertsimas
  • Dick den Hertog
  • Jean Pauphilet
  • Jianzhe Zhen
    • Categories Convex Optimization, Robust Optimization Tags , , ,

    Robust convex constraints are difficult to handle, since finding the worst-case scenario is equivalent to maximizing a convex function. In this paper, we propose a new approach to deal with such constraints that unifies approaches known in the literature and extends them in a significant way. The extension is either obtaining better solutions than the … Read more

    Adjustable Robust Optimization via Fourier-Motzkin Elimination

  • Dick den Hertog
  • Melvyn Sim
  • Jianzhe Zhen
    • Categories Robust Optimization Tags , , ,

    We demonstrate how adjustable robust optimization (ARO) problems with fixed recourse can be casted as static robust optimization problems via Fourier-Motzkin elimination (FME). Through the lens of FME, we characterize the structures of the optimal decision rules for a broader class of ARO problems. A scheme based on a blending of classical FME and a … Read more