Stochastic Programming

A Stochastic Electricity Market Clearing Formulation with Consistent Pricing Properties

  • Mihai Anitescu
  • John Birge
  • Kibaek Kim
  • Victor M. Zavala
    • Categories Applications - OR and Management Sciences, Convex and Nonsmooth Optimization, Stochastic Programming

    We argue that deterministic market clearing formulations introduce arbitrary distortions between day-ahead and expected real-time prices that bias economic incentives and block diversi cation. We extend and analyze the stochastic clearing formulation proposed by Pritchard et al. (2010) in which the social surplus function induces penalties between day-ahead and real-time quantities. We prove that the formulation … Read more

    A robust optimization model for the risk averse reservoir management problem

  • Erick Delage
  • Charles Gauvin
  • Michel Gendreau
    • Categories Applications - Science and Engineering, Robust Optimization, Stochastic Programming Tags , , , ,

    This paper presents a new formulation for the risk averse stochastic reservoir management problem. Using recent advances in robust optimization and stochastic programming, we propose a dynamic, multi-objective model based on minimization of a multidimensional risk measure associated with floods and droughts for a hydro-electrical complex. We present our model and then identify approximate solutions … Read more

    On Solving General Two-Stage Stochastic Programs

  • Manish Bansal
  • Sanjay Mehrotra
    • Categories Cutting Plane Approaches, Stochastic Programming

    We study general two-stage stochastic programs and present conditions under which the second stage programs can be convexified. This allows us to relax the restrictions, such as integrality, binary, semi-continuity, and many others, on the second stage variables in certain situations. Next, we introduce two-stage stochastic disjunctive programs (TSS-DPs) and extend Balas’s linear programming equivalent … Read more

    Robust Multicriteria Risk-Averse Stochastic Programming Models

  • Simge Küçükyavuz
  • Nilay Noyan
  • Xiao Liu
    • Categories Stochastic Programming

    In this paper, we study risk-averse models for multicriteria optimization problems under uncertainty. We use a weighted sum-based scalarization and take a robust approach by considering a set of scalarization vectors to address the ambiguity and inconsistency in the relative weights of each criterion. We model the risk aversion of the decision makers via the … Read more

    Stochastically Constrained Simulation Optimization On Integer-Ordered Spaces: The cgR-SPLINE Algorithm

  • Kalyani Nagaraj
  • Raghu Pasupathy
    • Categories Global Optimization, Integer Programming, Stochastic Programming Tags , ,

    We consider the problem of identifying the solution(s) to an optimization problem whose domain is a subset of the integer lattice, and whose objective and constraint functions can only be observed using a stochastic simulation. Such problems seem particularly prevalent (see www.simopt.org) within service systems having capacity or service-level constraints. We present cgR-SPLINE — a … Read more

    Distributionally Robust Logistic Regression

  • Daniel Kuhn
  • Peyman Mohajerin Esfahani
  • Soroosh Shafieezadeh-Abadeh
    • Categories Robust Optimization, Stochastic Programming Tags , ,

    This paper proposes a distributionally robust approach to logistic regression. We use the Wasserstein distance to construct a ball in the space of probability distributions centered at the uniform distribution on the training samples. If the radius of this ball is chosen judiciously, we can guarantee that it contains the unknown data-generating distribution with high … Read more

    Distributionally robust chance-constrained games: Existence and characterization of Nash equilibrium

  • Oualid Jouini
  • Abdel Lisser
  • Vikas Vikram Singh
    • Categories Game Theory, Stochastic Programming Tags , , , ,

    We consider an n-player finite strategic game. The payoff vector of each player is a random vector whose distribution is not completely known. We assume that the distribution of a random payoff vector of each player belongs to a distributional uncertainty set. We define a distributionally robust chance-constrained game using worst-case chance constraint. We consider … Read more

    Stability Analysis for Mathematical Programs with Distributionally Robust Chance Constraint

  • Shaoyan Guo
  • Huifu Xu
  • Liwei Zhang
    • Categories Robust Optimization, Stochastic Programming Tags , , ,

    Stability analysis for optimization problems with chance constraints concerns impact of variation of probability measure in the chance constraints on the optimal value and optimal solutions and research on the topic has been well documented in the literature of stochastic programming. In this paper, we extend such analysis to optimization problems with distributionally robust chance … Read more

    Tight second-stage formulations in two-stage stochastic mixed integer programs

  • Manish Bansal
  • Kuo-Ling Huang
  • Sanjay Mehrotra
    • Categories Cutting Plane Approaches, Production and Logistics, Stochastic Programming Tags , , , , , ,

    We study two-stage stochastic mixed integer programs (TSS-MIPs) with integer variables in the second stage. We show that under suitable conditions, the second stage MIPs can be convexified by adding parametric cuts a priori. As special cases, we extend the results of Miller and Wolsey (Math Program 98(1):73-88, 2003) to TSS-MIPs. Furthermore, we consider second … Read more

    Quantitative Stability Analysis for Distributionally Robust Optimization With Moment Constraints

  • Huifu Xu
  • Liwei Zhang
  • Jie Zhang
    • Categories Robust Optimization, Stochastic Programming Tags , , , ,

    In this paper we consider a broad class of distributionally robust optimization (DRO for short) problems where the probability of the underlying random variables depends on the decision variables and the ambiguity set is de ned through parametric moment conditions with generic cone constraints. Under some moderate conditions including Slater type conditions of cone constrained moment … Read more