multistage stochastic optimization

Sample Average Approximation and Model Predictive Control for Multistage Stochastic Optimization

  • Dominic S. T. Keehan
  • Andrew B. Philpott
  • Edward Anderson
    • Categories Robust Optimization, Stochastic Programming Tags , , ,

    Sample average approximation-based stochastic dynamic programming and model predictive control are two different methods of approaching multistage stochastic optimization. Model predictive control—despite a lack of theoretical backing—is often used instead of stochastic dynamic programming due to computational necessity. For settings where the stage reward is a convex function of the random terms, the stage dynamics … Read more

    A Multicut Approach to Compute Upper Bounds for Risk-Averse SDDP

  • Joaquim Dias Garcia
  • Mario Pereira
    • Categories Dynamic Programming, Energy, Stochastic Programming Tags , , , ,

    Stochastic Dual Dynamic Programming (SDDP) is a widely used and fundamental algorithm for solving multistage stochastic optimization problems. Although SDDP has been frequently applied to solve risk-averse models with the Conditional Value-at-Risk (CVaR), it is known that the estimation of upper bounds is a methodological challenge, and many methods are computationally intensive. In practice, this … Read more

    Convergence of Trajectory Following Dynamic Programming algorithms for multistage stochastic problems without finite support assumptions

  • Maël Forcier
  • Vincent Leclère
    • Categories Dynamic Programming, Stochastic Programming Tags , ,

    We introduce a class of algorithms, called Trajectory Following Dynamic Programming (TFDP) algorithms, that iteratively refines approximation of cost-to-go functions of multistage stochastic problems with independent random variables. This framework encompasses most variants of the Stochastic Dual Dynamic Programming algorithm. Leveraging a Lipschitz assumption on the expected cost-to-go functions, we provide a new convergence and … Read more

    On solving large-scale multistage stochastic problems with a new specialized interior-point approach

  • Jordi Castro
  • Laureano F. Escudero
  • Juan F. Monge
    • Categories Linear, Cone and Semidefinite Programming, Stochastic Programming Tags , , , , ,

    A novel approach based on a specialized interior-point method (IPM) is presented for solving large-scale stochastic multistage continuous optimization problems, which represent the uncertainty in strategic multistage and operational two-stage scenario trees, the latter being rooted at the strategic nodes. This new solution approach considers a split-variable formulation of the strategic and operational structures, for … Read more

    Portfolio Optimization with Irreversible Long-Term Investments in Renewable Energy under Policy Risk: A Mixed-Integer Multistage Stochastic Model and a Moving-Horizon Approach

  • Nadine Gatzert
  • Martin Schmidt
  • Alexander Martin
  • Benjamin Seith
  • Nikolai Vogl
    • Categories (Mixed) Integer Linear Programming, Applications - OR and Management Sciences, Stochastic Programming Tags , , , ,

    Portfolio optimization is an ongoing hot topic of mathematical optimization and management science. Due to the current financial market environment with low interest rates and volatile stock markets, it is getting more and more important to extend portfolio optimization models by other types of investments than classical assets. In this paper, we present a mixed-integer … Read more

    Distributionally robust optimization with multiple time scales: valuation of a thermal power plant

  • Daniela Escobar
  • Martin Glanzer
  • Georg Ch. Pflug
  • Wim van Ackooij
    • Categories Dynamic Programming, Stochastic Programming Tags , , , , , ,

    The valuation of a real option is preferably done with the inclusion of uncertainties in the model, since the value depends on future costs and revenues, which are not perfectly known today. The usual value of the option is defined as the maximal expected (discounted) profit one may achieve under optimal management of the operation. … Read more

    Rectangular sets of probability measures

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

    In this paper we consider the notion of rectangularity of a set of probability measures, introduced in Epstein and Schneider (2003), from a somewhat different point of view. We define rectangularity as a property of dynamic decomposition of a distributionally robust stochastic optimization problem and show how it relates to the modern theory of coherent … Read more