robust optimization

Distributionally Robust Joint Chance Constraints with Second-Order Moment Information

  • Daniel Kuhn
  • Berc Rustem
  • Steve Zymler
    • Categories Robust Optimization Tags , ,

    We develop tractable semidefinite programming (SDP) based approximations for distributionally robust individual and joint chance constraints, assuming that only the first- and second-order moments as well as the support of the uncertain parameters are given. It is known that robust chance constraints can be conservatively approximated by Worst-Case Conditional Value-at-Risk (CVaR) constraints. We first prove … Read more

    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

    Bilevel Derivative-Free Optimization and its Application to Robust Optimization

  • Andrew R. Conn
  • Luis Nunes Vicente
    • Categories Nonlinear Optimization Tags , , , , ,

    We address bilevel programming problems when the derivatives of both the upper and the lower level objective functions are unavailable. The core algorithms used for both levels are trust-region interpolation-based methods, using minimum Frobenius norm quadratic models when the number of points is smaller than the number of basis components. We take advantage of the … 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

    Nonconvex Robust Optimization

  • Kwong Meng Teo
    • Categories Applications - Science and Engineering, Constrained Nonlinear Optimization, Robust Optimization Tags , , , , , ,

    We propose a novel robust optimization technique, which is applicable to nonconvex and simulation-based problems. Robust optimization finds decisions with the best worst-case performance under uncertainty. If constraints are present, decisions should also be feasible under perturbations. In the real-world, many problems are nonconvex and involve computer-based simulations. In these applications, the relationship between decision … Read more

    Two-Stage Robust Unit Commitment Problem

  • Yongpei Guan
  • Muhong Zhang
    • Categories Robust Optimization Tags , , ,

    As an energy market transforms from a regulated market to a deregulated one, the demands for a power plant are highly uncertain. In this paper, we study a two-stage robust optimization formulation and provide a tractable solution approach for the problem. The computational experiments show the effectiveness of our approach. ArticleDownload View PDF

    Robust Software Partitioning with Multiple Instantiation

  • Daniel Kuhn
  • Wayne Luk
  • Simon Spacey
  • Wolfram Wiesemann
    • Categories Robust Optimization Tags , , ,

    The purpose of software partitioning is to assign code segments of a given computer program to a range of execution locations such as general purpose processors or specialist hardware components. These execution locations differ in speed, communication characteristics, and in size. In particular, hardware components offering high speed tend to accommodate only few code segments. … Read more

    On the Power of Robust Solutions in Two-Stage Stochastic and Adaptive Optimization Problems

  • Dimitris Bertsimas
  • Vineet Goyal
    • Categories Robust Optimization, Stochastic Programming Tags , , , ,

    We consider a two-stage mixed integer stochastic optimization problem and show that a static robust solution is a good approximation to the fully-adaptable two-stage solution for the stochastic problem under fairly general assumptions on the uncertainty set and the probability distribution. In particular, we show that if the right hand side of the constraints is … Read more