robust optimization

Inner approximations for polynomial matrix inequalities and robust stability regions

  • Didier Henrion
  • Jean-Bernard Lasserre
    • Categories Robust Optimization, Semi-definite Programming Tags , , , , ,

    Following a polynomial approach, many robust fixed-order controller design problems can be formulated as optimization problems whose set of feasible solutions is modelled by parametrized polynomial matrix inequalities (PMI). These feasibility sets are typically nonconvex. Given a parametrized PMI set, we provide a hierarchy of linear matrix inequality (LMI) problems whose optimal solutions generate inner … Read more

    Planning Wireless Networks with Demand Uncertainty using Robust Optimization

  • Grit Claßen
  • Arie M.C.A. Koster
  • Anke Schmeink
    • Categories Robust Optimization, Telecommunications Tags , ,

    An optimal planning of future wireless networks is fundamental to satisfy rising traffic demands jointly with the utilization of sophisticated techniques, such as OFDMA. Current methods for this task require a static model of the problem. However, uncertainty of data arises frequently in wireless networks, e. g., fluctuat- ing bit rate requirements. In this paper, … Read more

    Models and Algorithms for Distributionally Robust Least Squares Problems

  • Sanjay Mehrotra
  • He Zhang
    • Categories Robust Optimization, Second-Order Cone Programming, Semi-definite Programming Tags , ,

    We present different robust frameworks using probabilistic ambiguity descriptions of the input data in the least squares problems. The three probability ambiguity descriptions are given by: (1) confidence interval over the first two moments; (2) bounds on the probability measure with moments constraints; (3) confidence interval over the probability measure by using the Kantorovich probability … Read more

    Affine recourse for the robust network design problem: between static and dynamic routing

  • Michael Poss
  • Christian Raack
    • Categories Combinatorial Optimization, Network Optimization, Robust Optimization Tags , , , , ,

    Affinely-Adjustable Robust Counterparts provide tractable alternatives to (two-stage) robust programs with arbitrary recourse. We apply them to robust network design with polyhedral demand uncertainty, introducing the affine routing principle. We compare the affine routing to the well-studied static and dynamic routing schemes for robust network design. All three schemes are embedded into the general framework … 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

    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