Stochastic Programming

Complexity of Bilevel Coherent Risk Programming

  • Jonathan Eckstein
    • Categories Stochastic Programming Tags , ,

    This paper considers a bilevel programming approach to applying coherent risk measures to extended two-stage stochastic programming problems. This formulation technique avoids the time-inconsistency issues plaguing naive models and the incomposability issues which cause time-consistent formulations to have complicated, hard-to-explain objective functions. Unfortunately, the analysis here shows that such bilevel formulations, when using the standard … Read more

    The optimal harvesting problem under risk aversion

  • Bernardo K. Pagnoncelli
  • Adriana Piazza
    • Categories Applications - OR and Management Sciences, Stochastic Programming Tags , , ,

    We study the exploitation of a one species forest plantation when timber price is uncertain. The work focuses on providing optimality conditions for the optimal harvesting policy in terms of the parameters of the price process and the discount factor. We use risk averse stochastic dynamic programming and use the Conditional Value-at-Risk (CVaR) as our … Read more

    Risk-Averse Control of Undiscounted Transient Markov Models

  • Özlem Cavus
  • Andrzej Ruszczyński
    • Categories Dynamic Programming, Stochastic Programming

    We use Markov risk measures to formulate a risk-averse version of the undiscounted total cost problem for a transient controlled Markov process. We derive risk-averse dynamic programming equations and we show that a randomized policy may be strictly better than deterministic policies, when risk measures are employed. We illustrate the results on an optimal stopping … Read more

    Stochastic Optimization Approach to Water Management in Cooling-Constrained Power Plants

  • Emil M. Constantinescu
  • Victor M. Zavala
  • Urmila Diwekar
  • Juan M. Salazar
    • Categories Applications - OR and Management Sciences, Constrained Nonlinear Optimization, Stochastic Programming

    We propose a stochastic optimization framework to perform water management in coolingconstrained power plants. The approach determines optimal set-points to maximize power output in the presence of uncertain weather conditions and water intake constraints. Weather uncertainty is quantified in the form of ensembles using the state-of-the-art numerical weather prediction model WRF. The framework enables us … Read more

    Level Bundle Methods for oracles with on-demand accuracy

  • Welington de Oliveira
  • Claudia Sagastizábal
    • Categories Convex and Nonsmooth Optimization, Stochastic Programming Tags , , ,

    For nonsmooth convex optimization, we consider level bundle methods built using an oracle that computes values for the objective function and a subgradient at any given feasible point. For the problems of interest, the exact oracle information is computable, but difficult to obtain. In order to save computational effort the oracle can provide estimations with … Read more

    Decomposition Algorithms with Parametric Gomory Cuts for Two-Stage Stochastic Integer Programs

  • Dinakar Gade
  • Simge Küçükyavuz
  • Suvrajeet Sen
    • Categories Stochastic Programming Tags , , , , ,

    We consider a class of two-stage stochastic integer programs with binary variables in the first stage and general integer variables in the second stage. We develop decomposition algorithms akin to the L-shaped or Benders methods by utilizing Gomory cuts to obtain iteratively tighter approximations of the second-stage integer programs. We show that the proposed methodology … Read more

    Asymptotic Analysis of Sample Average Approximation for Stochastic Optimization Problems with Joint Chance Constraints via CVaR/DC Approximations

  • Hailin Sun
  • Huifu Xu
  • Yong Wang
    • Categories Applications - OR and Management Sciences, Stochastic Programming Tags , , , , ,

    Conditional Value at Risk (CVaR) has been recently used to approximate a chance constraint. In this paper, we study the convergence of stationary points when sample average approximation (SAA) method is applied to a CVaR approximated joint chance constrained stochastic minimization problem. Specifically, we prove, under some moderate conditions, that optimal solutions and stationary points … Read more

    Exact Penalization, Level Function Method and Modified Cutting-Plane Method for Stochastic Programs with Second Order Stochastic Dominance Constraints

  • Rudabeh Meskarian
  • Hailin Sun
  • Huifu Xu
  • Yong Wang
    • Categories Finance and Economics, Stochastic Programming Tags , , ,

    Level function methods and cutting plane methods have been recently proposed to solve stochastic programs with stochastic second order dominance (SSD) constraints. A level function method requires an exact penalization setup because it can only be applied to the objective function, not the constraints. Slater constraint qualification (SCQ) is often needed for deriving exact penalization. … Read more

    Solving multi-stage stochastic mixed integer linear programs by the dual dynamic programming approach

  • Zhihao Cen
    • Categories Applications - OR and Management Sciences, Cutting Plane Approaches, Stochastic Programming

    We consider a model of medium-term commodity contracts management. Randomness takes place only in the prices on which the commodities are exchanged, whilst state variable is multi-dimensional, and decision variable is integer. In our previous article, we proposed an algorithm based on the quantization of random process and a dual dynamic programming type approach to … Read more

    Stochastic first order methods in smooth convex optimization.

  • Olivier Devolder
    • Categories Convex Optimization, Stochastic Programming Tags , , , , , ,

    In this paper, we are interested in the development of efficient first-order methods for convex optimization problems in the simultaneous presence of smoothness of the objective function and stochasticity in the first-order information. First, we consider the Stochastic Primal Gradient method, which is nothing else but the Mirror Descent SA method applied to a smooth … Read more