Stochastic Programming

Discrete Approximation of Two-Stage Stochastic and Distributionally Robust Linear Complementarity Problems

  • Xiaojun Chen
  • Hailin Sun
  • Huifu Xu
    • Categories Robust Optimization, Stochastic Programming Tags , , , ,

    In this paper, we propose a discretization scheme for the two-stage stochastic linear complementarity problem (LCP) where the underlying random data are continuously distributed. Under some moderate conditions, we derive qualitative and quantitative convergence for the solutions obtained from solving the discretized two-stage stochastic LCP (SLCP). We ex- plain how the discretized two-stage SLCP may … Read more

    Optimizing power generation in the presence of micro-grids

  • Boris Detienne
  • Michael Poss
  • De Boeck Jérome
  • Pan Stefania
  • Wim van Ackooij
    • Categories 0-1 Programming, Applications - Science and Engineering, Stochastic Programming Tags , , ,

    In this paper we consider energy management optimization problems in a future wherein an interaction with micro-grids has to be accounted for. We will model this interaction through a set of contracts between the generation companies owning centralized assets and the micro-grids. We will formulate a general stylized model that can, in principle, account for … Read more

    Revisiting Approximate Linear Programming Using a Saddle Point Approach

  • Qihang Lin
  • Selvaprabu Nadarajah
  • Negar Soheili
    • Categories Dynamic Programming, Semi-infinite Programming, Stochastic Programming Tags , , , , ,

    Approximate linear programs (ALPs) are well-known models for computing value function approximations (VFAs) of intractable Markov decision processes (MDPs) arising in applications. VFAs from ALPs have desirable theoretical properties, define an operating policy, and provide a lower bound on the optimal policy cost, which can be used to assess the suboptimality of heuristic policies. However, … Read more

    Robust Stochastic Optimization Made Easy with RSOME

  • Melvyn Sim
  • Peng Xiong
  • Zhi Chen
    • Categories Robust Optimization, Stochastic Programming Tags , ,

    We present a new distributionally robust optimization model called robust stochastic optimization (RSO), which unifies both scenario-tree based stochastic linear optimization and distributionally robust optimization in a practicable framework that can be solved using the state-of-the-art commercial optimization solvers. We also develop a new algebraic modeling package, RSOME to facilitate the implementation of RSO models. … Read more

    The Adaptive Sampling Gradient Method: Optimizing Smooth Functions with an Inexact Oracle

  • Fatemeh Hashemi
  • Raghu Pasupathy
  • Michael Taaffe
    • Categories Nonlinear Optimization, Optimization of Simulated Systems, Stochastic Programming Tags , ,

    Consider settings such as stochastic optimization where a smooth objective function $f$ is unknown but can be estimated with an \emph{inexact oracle} such as quasi-Monte Carlo (QMC) or numerical quadrature. The inexact oracle is assumed to yield function estimates having error that decays with increasing oracle effort. For solving such problems, we present the Adaptive … Read more

    A Stochastic MPC Framework for Stationary Battery Systems

  • Kirk Drees
  • Victor M. Zavala
  • Mohammad ElBsat
  • Matthew Ellis
  • Ranjeet Kumar
  • Michael Wenzel
    • Categories Control Applications, Linear Programming, Stochastic Programming

    We present a stochastic model predictive control (MPC) framework to determine real-time commitments in energy and frequency regulation markets for a stationary battery system while simultaneously mitigating long-term demand charges for an attached load. The framework solves a two-stage stochastic program over a receding horizon that maximizes the expected profit and that factors in uncertainty … Read more

    Vector Transport-Free SVRG with General Retraction for Riemannian Optimization: Complexity Analysis and Practical Implementation

  • Bo Jiang
  • Shiqian Ma
  • Anthony Man-Cho So
  • Shuzhong Zhang
    • Categories Constrained Nonlinear Optimization, Stochastic Programming Tags , , , ,

    In this paper, we propose a vector transport-free stochastic variance reduced gradient (SVRG) method with general retraction for empirical risk minimization over Riemannian manifold. Existing SVRG methods on manifold usually consider a specific retraction operation, and involve additional computational costs such as parallel transport or vector transport. The vector transport-free SVRG with general retraction we … Read more

    Multicut decomposition methods with cut selection for multistage stochastic programs

  • Michelle Bandarra
  • Vincent Guigues
    • Categories Stochastic Programming

    We introduce a variant of Multicut Decomposition Algorithms (MuDA), called CuSMuDA (Cut Selection for Multicut Decomposition Algorithms), for solving multistage stochastic linear programs that incorporates strategies to select the most relevant cuts of the approximate recourse functions. We prove the convergence of the method in a finite number of iterations and use it to solve … Read more

    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