Robust Optimization

Chance-Constrained Linear Matrix Inequalities with Dependent Perturbations: A Safe Tractable Approximation Approach

  • Sin-Shuen Cheung
  • Anthony Man-Cho So
  • Kuncheng Wang
    • Categories Robust Optimization Tags , ,

    The wide applicability of chance-constrained programming, together with advances in convex optimization and probability theory, has created a surge of interest in finding efficient methods for processing chance constraints in recent years. One of the successes is the development of so-called safe tractable approximations of chance-constrained programs, where a chance constraint is replaced by a … Read more

    Global Stability Analysis of Fluid Flows using Sum-of-Squares

  • Sergei Chernyshenko
  • Paul J. Goulart
    • Categories Basic Sciences Applications, Optimization of Systems modeled by PDEs, Robust Optimization

    This paper introduces a new method for proving global stability of fluid flows through the construction of Lyapunov functionals. For finite dimensional approximations of fluid systems, we show how one can exploit recently developed optimization methods based on sum-of-squares decomposition to construct a polynomial Lyapunov function. We then show how these methods can be extended … Read more

    Minimax and risk averse multistage stochastic programming

  • Alexander Shapiro
    • Categories Dynamic Programming, Robust Optimization, Stochastic Programming Tags , , , , , ,

    In this paper we study relations between the minimax, risk averse and nested formulations of multistage stochastic programming problems. In particular, we discuss conditions for time consistency of such formulations of stochastic problems. We also describe a connection between law invariant coherent risk measures and the corresponding sets of probability measures in their dual representation. … Read more

    Dynamic programming approach to adjustable robust optimization

  • Alexander Shapiro
    • Categories Robust Optimization, Stochastic Programming Tags , , , , ,

    In this paper we consider the adjustable robust approach to multistage optimization, for which we derive dynamic programming equations. We also discuss this from a point of view of risk averse stochastic programming. As an example we consider a robust formulation of the classical inventory model and show that, similar to the risk neutral case, … Read more

    Convex Graph Invariants

  • Venkat Chandrasekaran
  • Pablo A. Parrilo
  • Alan S. Willsky
    • Categories Convex Optimization, Graphs and Matroids, Robust Optimization

    The structural properties of graphs are usually characterized in terms of invariants, which are functions of graphs that do not depend on the labeling of the nodes. In this paper we study convex graph invariants, which are graph invariants that are convex functions of the adjacency matrix of a graph. Some examples include functions of … Read more

    A constraint sampling approach for multi-stage robust optimization

  • Daniel Kuhn
  • Berc Rustem
  • Phebe Vayanos
    • Categories Robust Optimization Tags , , ,

    We propose a tractable approximation scheme for convex (not necessarily linear) multi-stage robust optimization problems. We approximate the adaptive decisions by finite linear combinations of prescribed basis functions and demonstrate how one can optimize over these decision rules at low computational cost through constraint randomization. We obtain a-priori probabilistic guarantees on the feasibility properties of … Read more

    Costs and benefits of robust optimization

  • Ralf Werner
    • Categories Robust Optimization Tags , ,

    In this exposition the robust counterpart approach by Ben-Tal, El Ghaoui and Nemirovski is investigated with respect to its costs and benefits, with the focus on the costs of robustification. Although robust optimization has gained more and more interest among both academics and practitioners and although this certainly represents a well-established theory, it is to … Read more

    Robust Timing of Markdowns

  • Daniela Caro
  • Aurelie Thiele
  • Michael Dziecichowicz
    • Categories Robust Optimization, Yield Management Tags , , ,

    We propose an approach to the timing of markdowns over a finite time horizon that does not require the precise knowledge of the underlying probabilities, instead relying on range forecasts for the arrival rates of the demand processes, and that captures the degree of the manager’s risk aversion through intuitive budget-of-uncertainty functions. These budget functions … Read more

    Robust Unit Commitment Problem with Demand Response and Wind Energy

  • Bo Zeng
  • Long Zhao
    • Categories Robust Optimization, Scheduling Tags , , , ,

    To improve the efficiency in power generation and to reduce the greenhouse gas emission, both Demand Response (DR) strategy and intermittent renewable energy have been proposed or applied in electric power systems. However, the uncertainty and the generation pattern in wind farms and the complexity of demand side management pose huge challenges in power system … Read more

    Two-Stage Robust Power Grid Optimization Problem

  • Ruiwei Jiang
  • Yongpei Guan
  • Guang Li
  • Muhong Zhang
    • Categories Applications - OR and Management Sciences, Robust Optimization Tags , , , ,

    Under the deregulated energy market environment, plus the integration of renewable energy generation, both the supply and demand of a power grid system are volatile and under uncertainty. Accordingly, a large amount of spinning reserve is required at each bus to maintain the reliability of the power grid system in the traditional approach. In this … Read more