stochastic programming

Generalized Decision Rule Approximations for Stochastic Programming via Liftings

  • Angelos Georghiou
  • Daniel Kuhn
  • Wolfram Wiesemann
    • Categories Robust Optimization Tags , , ,

    Stochastic programming provides a versatile framework for decision-making under uncertainty, but the resulting optimization problems can be computationally demanding. It has recently been shown that, primal and dual linear decision rule approximations can yield tractable upper and lower bounds on the optimal value of a stochastic program. Unfortunately, linear decision rules often provide crude approximations … Read more

    Optimal Stochastic Approximation Algorithms for Strongly Convex Stochastic Composite Optimization I: a Generic Algorithmic Framework

  • Saeed Ghadimi
  • Guanghui Lan
    • Categories Convex Optimization, Data-Mining, Stochastic Programming Tags , , , , ,

    In this paper we present a generic algorithmic framework, namely, the accelerated stochastic approximation (AC-SA) algorithm, for solving strongly convex stochastic composite optimization (SCO) problems. While the classical stochastic approximation (SA) algorithms are asymptotically optimal for solving differentiable and strongly convex problems, the AC-SA algorithm, when employed with proper stepsize policies, can achieve optimal or … Read more

    Multistage Stochastic Portfolio Optimisation in Deregulated Electricity Markets Using Linear Decision Rules

  • Daniel Kuhn
  • Paula Rocha
    • Categories Applications - OR and Management Sciences, Stochastic Programming Tags , , , ,

    The deregulation of electricity markets increases the financial risk faced by retailers who procure electric energy on the spot market to meet their customers’ electricity demand. To hedge against this exposure, retailers often hold a portfolio of electricity derivative contracts. In this paper, we propose a multistage stochastic mean-variance optimisation model for the management of … Read more

    On mixed integer reformulations of monotonic probabilistic programming problems with discrete distributions

  • Vladimir I. Norkin
    • Categories (Mixed) Integer Nonlinear Programming, Finance and Economics, Stochastic Programming Tags , , , , ,

    The paper studies large scale mixed integer reformulation approach to stochastic programming problems containing probability and quantile functions, under assumption of discreteness of the probability distribution involved. Jointly with general sample approximation technique and contemporary mixed integer programming solvers the approach gives a regular framework to solution of practical probabilistic programming problems. In the literature … Read more

    Models and Formulations for Multivariate Dominance Constrained Stochastic Programs

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

    Dentcheva and Ruszczynski recently proposed using a stochastic dominance constraint to specify risk preferences in a stochastic program. Such a constraint requires the random outcome resulting from one’s decision to stochastically dominate a given random comparator. These ideas have been extended to problems with multiple random outcomes, using the notion of positive linear stochastic dominance. … Read more

    Risk Adjusted Budget Allocation Models with Application in Homeland Security

  • Tito Homem-de-Mello
  • Jian Hu
  • Sanjay Mehrotra
    • Categories Multi-Criteria Optimization, Robust Optimization, Stochastic Programming Tags , , , , ,

    This paper presents and studies several models for multi-criterion budget allocation problems under uncertainty. We start by introducing a robust weighted objective model, which is developed further using the concept of stochastic dominance to incorporate risk averseness of the decision maker. A budget minimization variant of this model is also presented. We use a Sample … Read more

    A decomposition-based warm-start method for stochastic programming

  • Marco Colombo
  • Andreas Grothey
    • Categories Stochastic Programming Tags , ,

    In this paper we propose a warm-start technique for interior point methods applicable to multi-stage stochastic programming problems. The main idea is to generate an initial point for the interior point solver by decomposing the barrier problem associated with the deterministic equivalent at the sec- ond stage and using a concatenation of the solutions of … Read more

    A comparison of sample-based Stochastic Optimal Control methods

  • Pierre Girardeau
    • Categories Stochastic Programming Tags , ,

    In this paper, we compare the performance of two scenario-based numerical methods to solve stochastic optimal control problems: scenario trees and particles. The problem consists in finding strategies to control a dynamical system perturbed by exogenous noises so as to minimize some expected cost along a discrete and finite time horizon. We introduce the Mean … Read more

    Fenchel Decomposition for Stochastic Mixed-Integer Programming

  • Lewis Ntaimo
    • Categories Stochastic Programming Tags , , , ,

    This paper introduces a new cutting plane method for two-stage stochastic mixed-integer programming (SMIP) called Fenchel decomposition (FD). FD uses a class of valid inequalities termed, FD cuts, which are derived based on Fenchel cutting planes from integer programming. First, we derive FD cuts based on both the first and second-stage variables, and devise an … Read more

    Analysis of Stochastic Dual Dynamic Programming Method

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

    In this paper we discuss statistical properties and rates of convergence of the Stochastic Dual Dynamic Programming (SDDP) method applied to multistage linear stochastic programming problems. We assume that the underline data process is stagewise independent and consider the framework where at first a random sample from the original (true) distribution is generated and consequently … Read more