dynamic equations

Risk averse stochastic programming: time consistency and optimal stopping

  • Alois Pichler
  • Alexander Shapiro
    • Categories Dynamic Programming, Stochastic Programming Tags , , , , ,

    Bellman formulated a vague principle for optimization over time, which characterizes optimal policies by stating that a decision maker should not regret previous decisions retrospectively. This paper addresses time consistency in stochastic optimization. The problem is stated in generality first. The paper discusses time consistent decision-making by addressing risk measures which are recursive, nested, dynamically … Read more

    Tutorial on risk neutral, distributionally robust and risk averse multistage stochastic programming

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

    In this tutorial we discuss several aspects of modeling and solving multistage stochastic programming problems. In particular we discuss distributionally robust and risk averse approaches to multistage stochastic programming, and the involved concept of time consistency. This tutorial is aimed at presenting a certain point of view of multistage stochastic programming, and can be viewed … Read more

    Interchangeability principle and dynamic equations in risk averse stochastic programming

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

    In this paper we consider interchangeability of the minimization operator with monotone risk functionals. In particular we discuss the role of strict monotonicity of the risk functionals. We also discuss implications to solutions of dynamic programming equations of risk averse multistage stochastic programming problems. ArticleDownload View PDF

    Worst-case-expectation approach to optimization under uncertainty

  • Joari Paulo da Costa
  • Alexander Shapiro
  • Murilo Pereira Soares
  • Wajdi Tekaya
    • Categories Applications - OR and Management Sciences, Robust Optimization, Stochastic Programming Tags , , , , , , , ,

    In this paper we discuss multistage programming with the data process subject to uncertainty. We consider a situation were the data process can be naturally separated into two components, one can be modeled as a random process, with a specified probability distribution, and the other one can be treated from a robust (worst case) point … Read more

    Risk neutral and risk averse Stochastic Dual Dynamic Programming method

  • Joari Paulo da Costa
  • Alexander Shapiro
  • Murilo Pereira Soares
  • Wajdi Tekaya
    • Categories Dynamic Programming, Scheduling, Stochastic Programming Tags , , , , , ,

    In this paper we discuss risk neutral and risk averse approaches to multistage (linear) stochastic programming problems based on the Stochastic Dual Dynamic Programming (SDDP) method. We give a general description of the algorithm and present computational studies related to planning of the Brazilian interconnected power system. Citation ArticleDownload View PDF

    Minimax and risk averse multistage stochastic programming

  • Alexander Shapiro
    • Categories Dynamic Programming, Robust Optimization, Stochastic Programming Tags , , , , , ,

    In this paper we study relations between the minimax, risk averse and nested formulations of multistage stochastic programming problems. In particular, we discuss conditions for time consistency of such formulations of stochastic problems. We also describe a connection between law invariant coherent risk measures and the corresponding sets of probability measures in their dual representation. … Read more

    Dynamic programming approach to adjustable robust optimization

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

    In this paper we consider the adjustable robust approach to multistage optimization, for which we derive dynamic programming equations. We also discuss this from a point of view of risk averse stochastic programming. As an example we consider a robust formulation of the classical inventory model and show that, similar to the risk neutral case, … Read more