Robust Optimization

Dice-sion Making under Uncertainty: When Can a Random Decision Reduce Risk?

  • Erick Delage
  • Daniel Kuhn
  • Wolfram Wiesemann
    • Categories Robust Optimization, Stochastic Programming

    Stochastic programming and distributionally robust optimization seek deterministic decisions that optimize a risk measure, possibly in view of the most adverse distribution in an ambiguity set. We investigate under which circumstances such deterministic decisions are strictly outperformed by random decisions which depend on a randomization device producing uniformly distributed samples that are independent of all … 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

    A Tractable Approach for designing Piecewise Affine Policies in Two-stage Adjustable Robust Optimization

  • Aharon Ben-Tal
  • Omar El Housni
  • Vineet Goyal
    • Categories Robust Optimization Tags , ,

    We consider the problem of designing piecewise affine policies for two-stage adjustable robust linear optimization problems under right-hand side uncertainty. It is well known that a piecewise affine policy is optimal although the number of pieces can be exponentially large. A significant challenge in designing a practical piecewise affine policy is constructing good pieces of … Read more

    Online First-Order Framework for Robust Convex Optimization

  • Nam Ho-Nguyen
  • Fatma Kılınç-Karzan
    • Categories Constrained Nonlinear Optimization, Robust Optimization Tags , , ,

    Robust optimization (RO) has emerged as one of the leading paradigms to efficiently model parameter uncertainty. The recent connections between RO and problems in statistics and machine learning domains demand for solving RO problems in ever more larger scale. However, the traditional approaches for solving RO formulations based on building and solving robust counterparts or … Read more

    Frechet inequalities via convex optimization

  • Paul Embrechts
  • Paul J. Goulart
  • Bart Paul Gerard Van Parys
    • Categories Convex Optimization, Infinite Dimensional Optimization, Robust Optimization Tags , ,

    Quantifying the risk carried by an aggregate position $S_d\defn\sum_{i=1}^d X_i$ comprising many risk factors $X_i$ is fundamental to both insurance and financial risk management. Frechet inequalities quantify the worst-case risk carried by the aggregate position given distributional information concerning its composing factors but without assuming independence. This marginal factor modeling of the aggregate position in … Read more

    Multi-Period Portfolio Optimization: Translation of Autocorrelation Risk to Excess Variance

  • Byung-Geun Choi
  • Ruiwei Jiang
  • Napat Rujeerapaiboon
    • Categories Finance and Economics, Robust Optimization, Stochastic Programming Tags , , ,

    Growth-optimal portfolios are guaranteed to accumulate higher wealth than any other investment strategy in the long run. However, they tend to be risky in the short term. For serially uncorrelated markets, similar portfolios with more robust guarantees have been recently proposed. This paper extends these robust portfolios by accommodating non-zero autocorrelations that may reflect investors’ … Read more

    Scalable Robust and Adaptive Inventory Routing

  • Dimitris Bertsimas
  • Swati Gupta
  • Joel Tay
    • Categories Robust Optimization, Transportation Tags , , , , ,

    We consider the finite horizon inventory routing problem with uncertain demand, where a supplier must deliver a particular commodity to its customers periodically, such that even under uncertain demand the customers do not stock out, e.g. supplying residential heating oil to customers. Current techniques that solve this problem with stochastic demand, robust or adaptive optimization … Read more

    Path Constraints in Tychastic and Unscented Optimal Control: Theory, Applications and Experimental Results

  • M. Karpenko
  • Isaac Ross
  • R. J. Proulx
    • Categories Applications - Science and Engineering, Robust Optimization, Stochastic Programming Tags , ,

    In recent papers, we have shown that a Lebesgue-Stieltjes optimal control theory forms the foundations for unscented optimal control. In this paper, we further our results by incorporating uncertain mixed state-control constraints in the problem formulation. We show that the integrated Hamiltonian minimization condition resembles a semi-infinite type mathematical programming problem. The resulting computational difficulties … Read more

    Effects of Uncertain Requirements on the Architecture Selection Problem

  • Somayeh Moazeni
  • Roshanak Nilchiani
    • Categories Applications - Science and Engineering, Multidisciplinary Design Optimization, Robust Optimization Tags , , ,

    The problem of identifying a specific design or architecture that allows to satisfy all the system requirements becomes more difficult when uncertainties are taken into account. When a requirement is subject to uncertainty there are a number approaches available to the system engineer, each one with its own benefits and disadvantages. Classical robust optimization is … Read more

    Distributionally Robust Optimization with Principal Component Analysis

  • Richard Chen
  • Habib Najm
  • Jean-Paul Watson
  • Jianqiang Cheng
  • Ali Pinar
  • Cosmin Safta
    • Categories Robust Optimization, Stochastic Programming Tags , , ,

    Distributionally robust optimization (DRO) is widely used, because it offers a way to overcome the conservativeness of robust optimization without requiring the specificity of stochastic optimization. On the computational side, many practical DRO instances can be equivalently (or approximately) formulated as semidefinite programming (SDP) problems via conic duality of the moment problem. However, despite being … Read more