Stochastic Programming

A Branch-and-Cut Decomposition Algorithm for Solving Chance-Constrained Mathematical Programs with Finite Support

  • James R. Luedtke
    • Categories Stochastic Programming Tags , , , ,

    We present a new approach for exactly solving chance-constrained mathematical programs having discrete distributions with nite support and random polyhedral constraints. Such problems have been notoriously difficult to solve due to nonconvexity of the feasible region, and most available methods are only able to nd provably good solutions in certain very special cases. Our approach … Read more

    Stochastic programs without duality gaps

  • Teemu Pennanen
  • Ari-Pekka Perkkiö
    • Categories Stochastic Programming Tags , ,

    This paper studies dynamic stochastic optimization problems parametrized by a random variable. Such problems arise in many applications in operations research and mathematical finance. We give sufficient conditions for the existence of solutions and the absence of a duality gap. Our proof uses extended dynamic programming equations, whose validity is established under new relaxed conditions … Read more

    Level methods uniformly optimal for composite and structured nonsmooth convex optimization

  • Guanghui Lan
    • Categories Convex and Nonsmooth Optimization, Linear, Cone and Semidefinite Programming, Stochastic Programming Tags , , , , ,

    The main goal of this paper is to develop uniformly optimal first-order methods for large-scale convex programming (CP). By uniform optimality we mean that the first-order methods themselves do not require the input of any problem parameters, but can still achieve the best possible iteration complexity bounds. To this end, we provide a substantial generalization … Read more

    Level methods uniformly optimal for composite and structured nonsmooth convex optimization

  • Guanghui Lan
    • Categories Convex and Nonsmooth Optimization, Linear, Cone and Semidefinite Programming, Stochastic Programming Tags , , , , ,

    The main goal of this paper is to develop uniformly optimal first-order methods for large-scale convex programming (CP). By uniform optimality we mean that the first-order methods themselves do not require the input of any problem parameters, but can still achieve the best possible iteration complexity bounds. To this end, we provide a substantial generalization … Read more

    Scalable Stochastic Optimization of Complex Energy Systems

  • Mihai Anitescu
  • Victor M. Zavala
  • Miles Lubin
  • Cosmin G. Petra
    • Categories Parallel Algorithms, Stochastic Programming Tags , , , ,

    We present a scalable approach and implementation for solving stochastic programming problems, with application to the optimization of complex energy systems under uncertainty. Stochastic programming is used to make decisions in the present while incorporating a model of uncertainty about future events (scenarios). These problems present serious computational difficulties as the number of scenarios becomes … Read more

    A Matrix-Free Approach For Solving The Gaussian Process Maximum Likelihood Problem

  • Mihai Anitescu
  • Jie Chen
  • Lei Wang
    • Categories Nonlinear Optimization, Statistics, Stochastic Programming Tags , , , , , ,

    Gaussian processes are the cornerstone of statistical analysis in many application ar- eas. Nevertheless, most of the applications are limited by their need to use the Cholesky factorization in the computation of the likelihood. In this work, we present a matrix-free approach for comput- ing the solution of the maximum likelihood problem involving Gaussian processes. … Read more

    A Matrix-Free Approach For Solving The Gaussian Process Maximum Likelihood Problem

  • Mihai Anitescu
    • Categories Nonlinear Optimization, Statistics, Stochastic Programming Tags , , , , , ,

    Gaussian processes are the cornerstone of statistical analysis in many application ar- eas. Nevertheless, most of the applications are limited by their need to use the Cholesky factorization in the computation of the likelihood. In this work, we present a matrix-free approach for comput- ing the solution of the maximum likelihood problem involving Gaussian processes. … Read more

    A Matrix-Free Approach For Solving The Gaussian Process Maximum Likelihood Problem

  • Mihai Anitescu
    • Categories Nonlinear Optimization, Statistics, Stochastic Programming Tags , , , , , ,

    Gaussian processes are the cornerstone of statistical analysis in many application ar- eas. Nevertheless, most of the applications are limited by their need to use the Cholesky factorization in the computation of the likelihood. In this work, we present a matrix-free approach for comput- ing the solution of the maximum likelihood problem involving Gaussian processes. … Read more

    Concepts and Applications of Stochastically Weighted Stochastic Dominance

  • Tito Homem-de-Mello
  • Jian Hu
  • Sanjay Mehrotra
    • Categories Applications - OR and Management Sciences, Multi-Criteria Optimization, Stochastic Programming Tags , , , ,

    Stochastic dominance theory provides tools to compare random entities. When comparing random vectors (say X and Y ), the problem can be viewed as one of multi-criterion decision making under uncertainty. One approach is to compare weighted sums of the components of these random vectors using univariate dominance. In this paper we propose new concepts … Read more

    SDDP for some interstage dependent risk averse problems and application to hydro-thermal planning

  • Vincent Guigues
    • Categories Stochastic Programming

    We consider interstage dependent stochastic linear programs where both the random right-hand side and the model of the underlying stochastic process have a special structure. Namely, for stage $t$, the right-hand side of the equality constraints (resp. the inequality constraints) is an affine function (resp. a given function $b_t$) of the process value for this … Read more