Stochastic Programming

Integrated Generator Maintenance and Operations Scheduling under Uncertain Failure Times

  • Shabbir Ahmed
  • Nagi Gebraeel
  • Murat Yildirim
  • Beste Basciftci
    • Categories Applications - Science and Engineering, Stochastic Programming Tags , ,

    Planning maintenances and operations is an important concern in power systems. Although optimization based joint maintenance and operations scheduling is studied in the literature, sudden disruptions due to random generator failures are not considered. In this paper we propose a stochastic mixed-integer programming approach for integrated condition-based maintenance and operations scheduling problem for a fleet … Read more

    An Investigation of Newton-Sketch and Subsampled Newton Methods

  • Albert S. Berahas
  • Raghu Bollapragada
  • Jorge Nocedal
    • Categories Convex Optimization, Nonlinear Optimization, Stochastic Programming Tags , , ,

    Sketching, a dimensionality reduction technique, has received much attention in the statistics community. In this paper, we study sketching in the context of Newton’s method for solving finite-sum optimization problems in which the number of variables and data points are both large. We study two forms of sketching that perform dimensionality reduction in data space: … Read more

    A Progressive Hedging Based Branch-and-Bound Algorithm for Stochastic Mixed-Integer Programs

  • Semih Atakan
  • Suvrajeet Sen
    • Categories Stochastic Programming

    Progressive Hedging (PH) is a well-known algorithm for solving multi-stage stochastic convex optimization problems. Most previous extensions of PH for stochastic mixed-integer programs have been implemented without convergence guarantees. In this paper, we present a new framework that shows how PH can be utilized while guaranteeing convergence to globally optimal solutions of stochastic mixed-integer convex … Read more

    Multistage Stochastic Unit Commitment Using Stochastic Dual Dynamic Integer Programming

  • Shabbir Ahmed
  • Xu Andy Sun
  • Jikai Zou
    • Categories Applications - Science and Engineering, Stochastic Programming Tags , ,

    Unit commitment (UC) is a key operational problem in power systems used to determine an optimal daily or weekly generation commitment schedule. Incorporating uncertainty in this already difficult mixed integer optimization problem introduces significant computational challenges. Most existing stochastic UC models consider either a two-stage decision structure, where the commitment schedule for the entire planning … Read more

    Interchangeability principle and dynamic equations in risk averse stochastic programming

  • Alexander Shapiro
    • Categories Stochastic Programming Tags , , , , ,

    In this paper we consider interchangeability of the minimization operator with monotone risk functionals. In particular we discuss the role of strict monotonicity of the risk functionals. We also discuss implications to solutions of dynamic programming equations of risk averse multistage stochastic programming problems. ArticleDownload View PDF

    From Data to Decisions: Distributionally Robust Optimization is Optimal

  • Daniel Kuhn
  • Bart Paul Gerard Van Parys
  • Peyman Mohajerin Esfahani
    • Categories Robust Optimization, Second-Order Cone Programming, Stochastic Programming Tags , , , , ,

    We study stochastic programs where the decision-maker cannot observe the distribution of the exogenous uncertainties but has access to a finite set of independent samples from this distribution. In this setting, the goal is to find a procedure that transforms the data to an estimate of the expected cost function under the unknown data-generating distribution, … Read more

    Lifted Polymatroid Inequalities for Mean-Risk Optimization with Indicator Variables

  • Alper Atamturk
  • Hyemin Jeon
    • Categories (Mixed) Integer Nonlinear Programming, Stochastic Programming Tags , , , ,

    We investigate a mixed 0-1 conic quadratic optimization problem with indicator variables arising in mean-risk optimization. The indicator variables are often used to model non-convexities such as fixed charges or cardinality constraints. Observing that the problem reduces to a submodular function minimization for its binary restriction, we derive three classes of strong convex valid inequalities … Read more

    Sample Average Approximation with Adaptive Importance Sampling

  • Mingbin Feng
  • Alvaro Maggiar
  • Jeremy Staum
  • Andreas Wächter
    • Categories Stochastic Programming Tags , , , ,

    We study sample average approximations under adaptive importance sampling in which the sample densities may depend on previous random samples. Based on a generic uniform law of large numbers, we establish uniform convergence of the sample average approximation to the true function. We obtain convergence of the optimal value and optimal solutions of the sample … Read more

    Distributionally Robust Newsvendor Problems with Variation Distance

  • Hamed Rahimian
  • Güzin Bayraksan
  • Tito Homem-de-Mello
    • Categories Stochastic Programming

    We use distributionally robust stochastic programs (DRSPs) to model a general class of newsvendor problems where the underlying demand distribution is unknown, and so the goal is to find an order quantity that minimizes the worst-case expected cost among an ambiguity set of distributions. The ambiguity set consists of those distributions that are not far—in … Read more

    Co-optimization of Demand Response and Reserve Offers for a Major Consumer

  • Miguel F. Anjos
  • Anthony Downward
  • Michael C. Ferris
  • Mahbubeh Habibian
  • Golbon Zakeri
    • Categories (Mixed) Integer Linear Programming, Applications - OR and Management Sciences, Stochastic Programming Tags , ,

    In this paper we present a stochastic optimization problem for a strategic major consumer who has flexibility over its consumption and can offer reserve. Our model is a bi-level optimization model (reformulated as a mixed-integer program) that embeds the optimal power flow problem, in which electricity and reserve are co-optimized. We implement this model for … Read more