Robust Optimization

Generalized Decision Rule Approximations for Stochastic Programming via Liftings

  • Angelos Georghiou
  • Daniel Kuhn
  • Wolfram Wiesemann
    • Categories Robust Optimization Tags , , ,

    Stochastic programming provides a versatile framework for decision-making under uncertainty, but the resulting optimization problems can be computationally demanding. It has recently been shown that, primal and dual linear decision rule approximations can yield tractable upper and lower bounds on the optimal value of a stochastic program. Unfortunately, linear decision rules often provide crude approximations … Read more

    Robust Optimization with Multiple Ranges: Theory and Application to R&D Project Selection

  • Ruken Duzgun
  • Aurelie Thiele
    • Categories Robust Optimization

    We present a robust optimization approach when the uncertainty in objective coefficients is described using multiple ranges for each coefficient. This setting arises when the value of the uncertain coefficients, such as cash flows, depends on an underlying random variable, such as the effectiveness of a new drug. Traditional robust optimization with a single range … Read more

    An Efficient Method to Estimate the Suboptimality of Affine Controllers

  • Paul J. Goulart
  • Daniel Kuhn
  • Michael J. Hadjiyiannis
    • Categories Control Applications, Robust Optimization Tags ,

    We consider robust output feedback control of time-varying, linear discrete-time systems operating over a finite horizon. For such systems, we consider the problem of designing robust causal controllers that minimize the expected value of a convex quadratic cost function, subject to mixed linear state and input constraints. Determination of an optimal control policy for such … Read more

    Robust Markov Decision Processes

  • Daniel Kuhn
  • Berc Rustem
  • Wolfram Wiesemann
    • Categories Dynamic Programming, Robust Optimization

    Markov decision processes (MDPs) are powerful tools for decision making in uncertain dynamic environments. However, the solutions of MDPs are of limited practical use due to their sensitivity to distributional model parameters, which are typically unknown and have to be estimated by the decision maker. To counter the detrimental effects of estimation errors, we consider … Read more

    Risk Adjusted Budget Allocation Models with Application in Homeland Security

  • Tito Homem-de-Mello
  • Jian Hu
  • Sanjay Mehrotra
    • Categories Multi-Criteria Optimization, Robust Optimization, Stochastic Programming Tags , , , , ,

    This paper presents and studies several models for multi-criterion budget allocation problems under uncertainty. We start by introducing a robust weighted objective model, which is developed further using the concept of stochastic dominance to incorporate risk averseness of the decision maker. A budget minimization variant of this model is also presented. We use a Sample … Read more

    Prediction Range Estimation from Noisy Raman Spectra

  • Matthew Glucksberg
  • Sanjay Mehrotra
  • Richard Van Duyne
  • Joseph Walsh
  • Lyandres Olga
    • Categories Basic Sciences Applications, Biomedical Applications, Robust Optimization Tags , , ,

    Inferences need to be drawn in biological systems using experimental multivariate data. The number of samples collected in many such experiments is small, and the data is noisy. We present and study the performance of a robust optimization (RO) model for such situations. We adapt this model to generate a minimum and a maximum estimation … Read more

    Locating a competitive facility in the plane with a robustness criterion

  • Rafael Blanquero
  • Emilio Carrizosa
  • Eligius M.T. Hendrix
    • Categories Facility Planning and Design, Global Optimization Applications, Robust Optimization Tags , , , , , ,

    A new continuous location model is presented and embedded in the literature on robustness in facility location. The multimodality of the model is investigated, and a branch and bound method based on dc optimization is described. Numerical experience is reported, showing that the developed method allows one to solve in a few seconds problems with … Read more

    An Efficient Decomposition Algorithm for Static, Stochastic, Linear and Mixed-Integer Linear Programs with Conditional-Value-at-Risk Constraints

  • Pu Huang
  • Dharmashankar Subramanian
    • Categories Applications - OR and Management Sciences, Robust Optimization

    We present an efficient decomposition algorithm for single-stage, stochastic linear programs, where conditional value at risk (CVaR) appears as a risk measure in multiple constraints. It starts with a well-known nonlinear, convex reformulation of conditional value at risk constraints, and establishes the connection to a combinatorially large polyhedral representation of the convex feasible set induced … Read more

    Worst-Case Violation of Sampled Convex Programs for Optimization with Uncertainty

  • Takafumi Kanamori
  • Akiko Takeda
    • Categories Robust Optimization Tags , , , ,

    Uncertain programs have been developed to deal with optimization problems including inexact data, i.e., uncertainty. A deterministic approach called robust optimization is commonly applied to solve these problems. Recently, Calafiore and Campi have proposed a randomized approach based on sampling of constraints, where the number of samples is determined so that only small portion of … Read more