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Variational Convergence of Bifunctions: Motivating Applications

  • Alejandro Jofré
  • Roger J.B. Wets
    • Categories Complementarity and Variational Inequalities, Convex and Nonsmooth Optimization, Game Theory Tags , , , , , , , , ,

    It’s shown that a number of variational problems can be cast as finding the maxinf-points (or minsup-points) of bivariate functions, coveniently abbreviated to bifunctions. These variational problems include: linear and nonlinear complementarity problems, fixed points, variational inequalities, inclusions, non-cooperative games, Walras and Nash equilibrium problems. One can then appeal to the theory of lopsided convergence … Read more

    On the Dynamic Stability of Electricity Markets

  • Mihai Anitescu
  • Victor M. Zavala
    • Categories Complementarity and Variational Inequalities, Dynamic Programming, Game Theory Tags , , , ,

    In this work, we present new insights into the dynamic stability of electricity markets. In particular, we discuss how short forecast horizons, incomplete gaming, and physical ramping constraints can give rise to stability issues. Using basic concepts of market efficiency, Lyapunov stability, and predictive control, we construct a new stabilizing market design. A numerical case … Read more

    Multiobjective DC Programming with Infinite Convex Constraints

  • Mark Goh
  • Shaojian Qu
  • Soonyi Wu
    • Categories Multi-Criteria Optimization, Nonsmooth Optimization, Semi-infinite Programming Tags , , , ,

    In this paper new results are established in multiobjective DC programming with infinite convex constraints ($MOPIC$ for abbr.) that are defined on Banach space (finite or infinite) with objectives given as the difference of convex functions subject to infinite convex constraints. This problem can also be called multiobjective DC semi-infinite and infinite programming, where decision … Read more

    Approximate Dynamic Programming with Bezier Curves/Surfaces for Top-percentile traffic routing

  • Andreas Grothey
  • Xinan Yang
    • Categories Dynamic Programming, Telecommunications Tags , , , , ,

    Multi-homing is used by Internet Service Provider (ISP) to connect to the Internet via different network providers. This study investigates the optimal routing strategy under multi-homing in the case where network providers charge ISPs according to top-percentile pricing (i.e. based on the $\theta$-th highest volume of traffic shipped). We call this problem the Top-percentile Traffic … 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 sampling algorithms for multi-stage stochastic programs with risk aversion

  • Vitor de Matos
  • Andrew B. Philpott
    • Categories Dynamic Programming, Stochastic Programming Tags , ,

    We consider the incorporation of a time-consistent coherent risk measure into a multi-stage stochastic programming model, so that the model can be solved using a SDDP-type algorithm. We describe the implementation of this algorithm, and study the solutions it gives for an application of hydro-thermal scheduling in the New Zealand electricity system. The performance of … Read more

    Optimal adaptive control of cascading power grid failures

  • Daniel Bienstock
    • Categories Control Applications, Optimization of Simulated Systems Tags , ,

    We describe experiments with parallel algorithms for computing adaptive controls for attenuating power grid cascading failures. Citation Columbia University, 2010 Article Download View Optimal adaptive control of cascading power grid failures

    Preconditioning and Globalizing Conjugate Gradients in Dual Space for Quadratically Penalized Nonlinear-Least Squares Problems

  • Serge Gratton
  • Philippe L. Toint
  • Selime Gürol
    • Categories Nonlinear Systems and Least-Squares, Optimization of Simulated Systems, Optimization of Systems modeled by PDEs Tags , , , , ,

    When solving nonlinear least-squares problems, it is often useful to regularize the problem using a quadratic term, a practice which is especially common in applications arising in inverse calculations. A solution method derived from a trust-region Gauss-Newton algorithm is analyzed for such applications, where, contrary to the standard algorithm, the least-squares subproblem solved at each … Read more

    Cost-sharing mechanisms for scheduling under general demand settings

  • Sindhura Balireddi
  • Nelson A. Uhan
    • Categories Game Theory, Scheduling

    We investigate cost-sharing mechanisms for scheduling cost-sharing games. We assume that the demand is general—that is, each player can be allocated one of several levels of service. We show how to design mechanisms for these games that are weakly group strategyproof, approximately budget-balanced, and approximately efficient, using approximation algorithms for the underlying scheduling problems. We … Read more

    Minimum cost subset selection with two competing agents

  • Gaia Nicosia
  • Ulrich Pferschy
  • Andrea Pacifici
    • Categories Combinatorial Optimization, Game Theory Tags , , , , ,

    We address an optimization problem in which two agents, each with a set of weighted items, compete in order to minimize the total weight of their solution sets. The latter are built according to a sequential game consisting in a fixed number of rounds. In every round each agent submits one item that may be … Read more