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High Throughput Computing for Massive Scenario Analysis and Optimization to Minimize Cascading Blackout Risk

  • Eric Anderson
  • Jeff Linderoth
    • Categories Applications - OR and Management Sciences, Applications - Science and Engineering, Optimization of Simulated Systems

    We describe a simulation-based optimization method that allocates additional capacity to transmission lines in order to minimize the expected value of the load shed due to a cascading blackout. Estimation of the load-shed distribution is accomplished via the ORNL-PSerc-Alaska (OPA) simulation model, which solves a sequence of linear programs. Key to achieving an effective algorithm … Read more

    A Linear Scalarization Proximal Point Method for Quasiconvex Multiobjective Minimization

  • H. C. F. Apolinário
  • Paulo Roberto Oliveira
  • Erik Alex Papa Quiroz
  • Kely Diana Villacorta
    • Categories Multi-Criteria Optimization, Nonlinear Optimization, Unconstrained Optimization

    In this paper we propose a linear scalarization proximal point algorithm for solving arbitrary lower semicontinuous quasiconvex multiobjective minimization problems. Under some natural assumptions and using the condition that the proximal parameters are bounded we prove the convergence of the sequence generated by the algorithm and when the objective functions are continuous, we prove the … Read more

    A Linear Scalarization Proximal Point Method for Quasiconvex Multiobjective Minimization

  • H. C. F. Apolinário
  • Paulo Roberto Oliveira
  • Erik Alex Papa Quiroz
  • Kely Diana Villacorta
    • Categories Multi-Criteria Optimization, Nonlinear Optimization, Unconstrained Optimization

    In this paper we propose a linear scalarization proximal point algorithm for solving arbitrary lower semicontinuous quasiconvex multiobjective minimization problems. Under some natural assumptions and using the condition that the proximal parameters are bounded we prove the convergence of the sequence generated by the algorithm and when the objective functions are continuous, we prove the … Read more

    Strong slopes of a vector-valued map and applications in the study of error bounds, weak sharp minima and calmness

  • Xuan Duc Ha Truong
    • Categories Multi-Criteria Optimization Tags , , , , , ,

    Using Hiriart-Urruty’s signed distance function, we present new definitions of strong slopes for a vector-valued map recently introduced in [E.M. Bednarczuk, A.Y., Kruger, Error bounds for vector-valued functions on metric spaces. Vietnam J. Math. 40 (2012), no. 2-3, 165-180]. With the new presentation, we are able to show that these slopes enjoy most properties of … Read more

    Distributionally robust chance-constrained games: Existence and characterization of Nash equilibrium

  • Oualid Jouini
  • Abdel Lisser
  • Vikas Vikram Singh
    • Categories Game Theory, Stochastic Programming Tags , , , ,

    We consider an n-player finite strategic game. The payoff vector of each player is a random vector whose distribution is not completely known. We assume that the distribution of a random payoff vector of each player belongs to a distributional uncertainty set. We define a distributionally robust chance-constrained game using worst-case chance constraint. We consider … Read more

    A Quantitative Comparison of Risk Measures

  • Alois Pichler
    • Categories Applications - OR and Management Sciences, Dynamic Programming, Stochastic Programming Tags ,

    The choice of a risk measure reflects a subjective preference of the decision maker in many managerial, or real world economic problem formulations. To evaluate the impact of personal preferences it is thus of interest to have comparisons with other risk measures at hand. This paper develops a framework for comparing different risk measures. We … Read more

    Nonstationary Direct Policy Search for Risk-Averse Stochastic Optimization

  • Belgacem Bouzaiene-Ayari
  • Somayeh Moazeni
  • Boris Defourny
  • Warren B. Powell
    • Categories Dynamic Programming, Parallel Algorithms, Stochastic Programming Tags , ,

    This paper presents an approach to non-stationary policy search for finite-horizon, discrete-time Markovian decision problems with large state spaces, constrained action sets, and a risk-sensitive optimality criterion. The methodology relies on modeling time variant policy parameters by a non-parametric response surface model for an indirect parametrized policy motivated by the Bellman equation. Through the interpolating … Read more

    Solving linear generalized Nash equilibrium problems numerically

  • Axel Dreves
  • Nathan Sudermann-Merx
    • Categories Game Theory Tags , , , ,

    This paper considers the numerical solution of linear generalized Nash equilibrium problems. Since many methods for nonlinear problems require the nonsingularity of some second order derivative, standard convergence conditions are not satisfied in our linear case. We provide new convergence criteria for a potential reduction algorithm that allow its application to linear generalized Nash equilibrium … Read more

    Variational Analysis and Applications to Group Dynamics

  • Antoine Soubeyran
  • Bao Q. Truong
    • Categories Applications - OR and Management Sciences, Multi-Criteria Optimization, Nonsmooth Optimization Tags , , , , ,

    In this paper, we establish a new version of Ekeland’s variational principle in a new setting of cone pseudo-quasimetric spaces. In constrast to metric spaces, we do not require that each forward Cauchy sequence is forward convergent and that each forward convergent sequence has the unique forward limit. The motivation of this paper comes from … Read more

    A Practical Scheme to Compute Pessimistic Bilevel Optimization Problem

  • Bo Zeng
    • Categories Complementarity and Variational Inequalities, Game Theory Tags ,

    In this paper, we present a new computation scheme for pessimistic bilevel optimization problem, which so far does not have any computational methods generally applicable yet. We first develop a tight relaxation and then design a simple scheme to ensure a feasible and optimal solution. Then, we discuss using this scheme to compute linear pessimistic … Read more