Stochastic Programming

Levenberg-Marquardt methods based on probabilistic gradient models and inexact subproblem solution, with application to data assimilation

  • Elhoucine Bergou
  • Serge Gratton
  • Luis Nunes Vicente
    • Categories Applications - Science and Engineering, Nonlinear Systems and Least-Squares, Stochastic Programming Tags , , , , , , ,

    The Levenberg-Marquardt algorithm is one of the most popular algorithms for the solution of nonlinear least squares problems. Motivated by the problem structure in data assimilation, we consider in this paper the extension of the classical Levenberg-Marquardt algorithm to the scenarios where the linearized least squares subproblems are solved inexactly and/or the gradient model is … Read more

    Symmetric confidence regions and confidence intervals for normal map formulations of stochastic variational inequalities

  • Shu Lu
    • Categories Complementarity and Variational Inequalities, Stochastic Programming Tags , , , , ,

    Stochastic variational inequalities (SVI) model a large class of equilibrium problems subject to data uncertainty, and are closely related to stochastic optimization problems. The SVI solution is usually estimated by a solution to a sample average approximation (SAA) problem. This paper considers the normal map formulation of an SVI, and proposes a method to build … Read more

    Individual confidence intervals for true solutions to stochastic variational inequalities

  • Amarjit Budhiraja
  • Shu Lu
  • Lamm Michael
    • Categories Complementarity and Variational Inequalities, Stochastic Programming

    Stochastic variational inequalities (SVI) provide a means for modeling various optimization and equilibrium problems where data are subject to uncertainty. Often it is necessary to estimate the true SVI solution by the solution of a sample average approximation (SAA) problem. This paper proposes three methods for building confidence intervals for components of the true solution, … Read more

    A Class of Randomized Primal-Dual Algorithms for Distributed Optimization

  • Jean-Christophe Pesquet
  • Audrey Repetti
    • Categories Convex Optimization, Nonsmooth Optimization, Stochastic Programming Tags , , , , , ,

    Based on a preconditioned version of the randomized block-coordinate forward-backward algorithm recently proposed in [Combettes,Pesquet,2014], several variants of block-coordinate primal-dual algorithms are designed in order to solve a wide array of monotone inclusion problems. These methods rely on a sweep of blocks of variables which are activated at each iteration according to a random rule, … Read more

    Robust Growth-Optimal Portfolios

  • Daniel Kuhn
  • Napat Rujeerapaiboon
  • Wolfram Wiesemann
    • Categories Robust Optimization, Stochastic Programming Tags ,

    The growth-optimal portfolio is designed to have maximum expected log-return over the next rebalancing period. Thus, it can be computed with relative ease by solving a static optimization problem. The growth-optimal portfolio has sparked fascination among finance professionals and researchers because it can be shown to outperform any other portfolio with probability 1 in the … Read more

    Toward Scalable Stochastic Unit Commitment – Part 1: Load Scenario Generation

  • Yonghan Feng
  • Jean-Paul Watson
  • Ignacio Rios
  • Sarah M. Ryan
  • Kai Spurkel
  • Roger J.B. Wets
  • David L. Woodruff
    • Categories Stochastic Programming

    Unit commitment decisions made in the day-ahead market and during subsequent reliability assessments are critically based on forecasts of load. Traditional, deterministic unit commitment is based on point or expectation-based load forecasts. In contrast, stochastic unit commitment relies on multiple load scenarios, with associated probabilities, that in aggregate capture the range of likely load time-series. … Read more

    Toward Scalable Stochastic Unit Commitment – Part 2: Solver Configuration and Performance Assessment

  • Kwok Cheung
  • Dinakar Gade
  • Cesar Silva-Monroy
  • Jean-Paul Watson
  • Sarah M. Ryan
  • Roger J.B. Wets
  • David L. Woodruff
    • Categories Stochastic Programming

    In this second portion of a two-part analysis of a scalable computational approach to stochastic unit commitment, we focus on solving stochastic mixed-integer programs in tractable run-times. Our solution technique is based on Rockafellar and Wets’ progressive hedging algorithm, a scenario-based decomposition strategy for solving stochastic programs. To achieve high-quality solutions in tractable run-times, we … Read more

    Chance-Constrained Multi-Terminal Network Design Problems

  • Yongjia Song
  • Minjiao Zhang
    • Categories Integer Programming, Network Optimization, Stochastic Programming Tags , , ,

    We consider a reliable network design problem under uncertain edge failures. Our goal is to select a minimum-cost subset of edges in the network to connect multiple terminals together with high probability. This problem can be seen as a stochastic variant of the Steiner tree problem. We propose a scenario-based Steiner cut formulation, and a … Read more

    Improving the integer L-shaped method

  • Shabbir Ahmed
  • Gustavo Angulo
  • Santanu S. Dey
    • Categories Integer Programming, Stochastic Programming Tags , , ,

    We consider the integer L-shaped method for two-stage stochastic integer programs. To improve the performance of the algorithm, we present and combine two strategies. First, to avoid time-consuming exact evaluations of the second-stage cost function, we propose a simple modification that alternates between linear and mixed-integer subproblems. Then, to better approximate the shape of the … Read more