Stochastic Programming

Adjoint Sensitivity Analysis for Numerical Weather Prediction: Applications to Power Grid Optimization

  • Alexandru Cioaca
  • Emil M. Constantinescu
  • Victor M. Zavala
    • Categories Constrained Nonlinear Optimization, Control Applications, Stochastic Programming Tags ,

    We present an approach to estimate adjoint sensitivities of economic metrics of relevance in the power grid with respect to physical weather variables using numerical weather prediction models. We demonstrate that this capability can significantly enhance planning and operations. We illustrate the method using a large-scale computational study where we compute sensitivities of the regional … Read more

    Sell or Hold: a simple two-stage stochastic combinatorial optimization problem

  • Shabbir Ahmed
  • Qie He
  • George L. Nemhauser
    • Categories Combinatorial Optimization, Integer Programming, Stochastic Programming

    There are $n$ individual assets and $k$ of them are to be sold over two stages. The first-stage prices are known and the second-stage prices have a known distribution. The sell or hold problem (SHP) is to determine which assets are to be sold at each stage to maximize the total expected revenue. We show … Read more

    Decision Making under Uncertainty when Preference Information is Incomplete

  • Benjamin Armbruster
  • Erick Delage
    • Categories Finance and Economics, Robust Optimization, Stochastic Programming Tags , , ,

    We consider the problem of optimal decision making under uncertainty but assume that the decision maker’s utility function is not completely known. Instead, we consider all the utilities that meet some criteria, such as preferring certain lotteries over certain other lotteries and being risk averse, s-shaped, or prudent. This extends the notion of stochastic dominance. … Read more

    A Polynomial-Time Solution Scheme for Quadratic Stochastic Programs

  • Daniel Kuhn
  • Paula Rocha
    • Categories Robust Optimization, Stochastic Programming Tags , , ,

    We consider quadratic stochastic programs with random recourse – a class of problems which is perceived to be computationally demanding. Instead of using mainstream scenario tree-based techniques, we reduce computational complexity by restricting the space of recourse decisions to those linear and quadratic in the observations, thereby obtaining an upper bound on the original problem. … Read more

    Probabilistic Set Covering with Correlations

  • Shabbir Ahmed
  • Dimitri J. Papageorgiou
    • Categories Integer Programming, Stochastic Programming Tags , , , ,

    We consider a probabilistic set covering problem where there is uncertainty regarding whether a selected set can cover an item, and the objective is to determine a minimum-cost combination of sets so that each item is covered with a pre-specified probability. To date, literature on this problem has focused on the special case in which … Read more

    The optimal harvesting problem with price uncertainty

  • Bernardo K. Pagnoncelli
  • Adriana Piazza
    • Categories Dynamic Programming, Stochastic Programming Tags , , ,

    In this paper we study the exploitation of a one species forest plantation when timber price is governed by a stochastic process. The work focuses on providing closed expressions for the optimal harvesting policy in terms of the parameters of the price process and the discount factor. We assume that harvest is restricted to mature … Read more

    HOGWILD!: A Lock-Free Approach to Parallelizing Stochastic Gradient Descent

  • Feng Niu
  • Christopher Re
  • Benjamin Recht
  • Stephen Wright
    • Categories Data-Mining, Nonlinear Optimization, Stochastic Programming Tags , , , ,

    Stochastic Gradient Descent (SGD) is a popular algorithm that can achieve state-of-the-art performance on a variety of machine learning tasks. Several researchers have recently proposed schemes to parallelize SGD, but all require performance-destroying memory locking and synchronization. This work aims to show using novel theoretical analysis, algorithms, and implementation that SGD can be implemented *without … Read more

    Convex relaxations of chance constrained optimization problems

  • Shabbir Ahmed
    • Categories Stochastic Programming Tags ,

    In this paper we develop convex relaxations of chance constrained optimization problems in order to obtain lower bounds on the optimal value. Unlike existing statistical lower bounding techniques, our approach is designed to provide deterministic lower bounds. We show that a version of the proposed scheme leads to a tractable convex relaxation when the chance … Read more

    A Bilevel Direct Search Method for Leader-Follower Optimization Problems and Applications

  • Gui-Hua Lin
  • Dali Zhang
    • Categories Game Theory, Other Topics, Stochastic Programming Tags , , , ,

    In the paper, we propose a bilevel direct search method for solving a type of leader-follower problems with each decision maker’s objective being a “black-box” function. First, we give a description for a leader-follower optimization problem. Then, we investigate a bilevel direct search method including two algorithms for combinatorially solving the upper and lower level … Read more

    Distributionally robust workforce scheduling in call centers with uncertain arrival rates

  • Shuangqing Liao
  • Jean-Philippe Vial
  • Christian van Delft
    • Categories Robust Optimization, Stochastic Programming

    Call center scheduling aims to set-up the workforce so as to meet target service levels. The service level depends on the mean rate of arrival calls, which fluctuates during the day and from day to day. The staff scheduling must adjust the workforce period per period during the day, but the flexibility in so doing … Read more