Dick den Hertog

Efficient methods for several classes of ambiguous stochastic programming problems under mean-MAD information

  • Dick den Hertog
  • Krzysztof Postek
  • Ward Romeijnders
  • Maarten H. van der Vlerk
    • Categories Robust Optimization, Stochastic Programming

    We consider decision making problems under uncertainty, assuming that only partial distributional information is available – as is often the case in practice. In such problems, the goal is to determine here-and-now decisions, which optimally balance deterministic immediate costs and worst-case expected future costs. These problems are challenging, since the worst-case distribution needs to be … Read more

    Adjustable robust strategies for flood protection

  • Dick den Hertog
  • Krzysztof Postek
  • Jarl Kind
  • Chris Pustjens
    • Categories Civil and Environmental Engineering Tags , , ,

    Flood protection is of major importance to many flood-prone regions and involves substantial investment and maintenance costs. Modern flood risk management requires often to determine a cost-efficient protection strategy, i.e., one with lowest possible long run cost and satisfying flood protection standards imposed by the regulator throughout the entire planning horizon. There are two challenges … Read more

    A universal and structured way to derive dual optimization problem formulations

  • Marleen Balvert
  • Dick den Hertog
  • Bram L. Gorissen
  • Cornelis Roos
    • Categories Convex Optimization Tags , , , ,

    The dual problem of a convex optimization problem can be obtained in a relatively simple and structural way by using a well-known result in convex analysis, namely Fenchel’s duality theorem. This alternative way of forming a strong dual problem is the subject in this paper. We recall some standard results from convex analysis and then … 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

    Robust optimization of dose-volume metrics for prostate HDR-brachytherapy incorporating target- and OAR volume delineation uncertainties

  • Marleen Balvert
  • Dick den Hertog
  • Aswin Hoffmann
    • Categories Biomedical Applications, Robust Optimization Tags , , , ,

    In radiation therapy planning, uncertainties in target volume definition yield a risk of underdosing the tumor. The classical way to prevent this in the context of external beam radiotherapy (EBRT) has been to expand the clinical target volume (CTV) with an isotropic margin to obtain the planning target volume (PTV). However, the EBRT-based PTV concept … Read more

    The impact of the existence of multiple adjustable robust solutions

  • Ruud C.M. Brekelmans
  • Frans J.C.T. de Ruiter
  • Dick den Hertog
    • Categories Applications - OR and Management Sciences, Robust Optimization

    In this note we show that multiple solutions exist for the production-inventory example in the seminal paper on adjustable robust optimization in [2]. All these optimal robust solutions have the same worst-case objective value, but the mean objective values differ up to 21.9% and for individual realizations this difference can be up to 59.4%. We … Read more

    Robust Dual Response Optimization

  • Dick den Hertog
  • Jack P.C. Kleijnen
  • Ihsan Yanıkoğlu
    • Categories Applications - OR and Management Sciences, Nonlinear Optimization, Robust Optimization

    This article presents a robust optimization reformulation of the dual response problem developed in response surface methodology. The dual response approach fits separate models for the mean and the variance, and analyzes these two models in a mathematical optimization setting. We use metamodels estimated from experiments with both controllable and environmental inputs. These experiments may … Read more

    When are static and adjustable robust optimization with constraint-wise uncertainty equivalent?

  • Dick den Hertog
  • Ahmadreza Marandi
    • Categories Robust Optimization Tags , , ,

    Adjustable Robust Optimization (ARO) yields, in general, better worst-case solutions than static Robust Optimization (RO). However, ARO is computationally more difficult than RO. In this paper, we derive conditions under which the worst-case objective values of ARO and RO problems are equal. We prove that if the uncertainty is constraint-wise and the adjustable variables lie … Read more

    Centered Solutions for Uncertain Linear Equations

  • Dick den Hertog
  • Jianzhe Zhen
    • Categories Robust Optimization

    Our contribution is twofold. Firstly, for a system of uncertain linear equations where the uncertainties are column-wise and reside in general convex sets, we show that the intersection of the set of possible solutions and any orthant is convex. We derive a convex representation of this intersection. Secondly, to obtain centered solutions for systems of … Read more

    Robust optimization with ambiguous stochastic constraints under mean and dispersion information

  • Aharon Ben-Tal
  • Dick den Hertog
  • Krzysztof Postek
  • Bertrand Melenberg
    • Categories Robust Optimization Tags , , ,

    In this paper we consider ambiguous stochastic constraints under partial information consisting of means and dispersion measures of the underlying random parameters. Whereas the past literature used the variance as the dispersion measure, here we use the mean absolute deviation from the mean (MAD). This makes it possible to use the old result of Ben-Tal … Read more