Stochastic Programming

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

    Time consistency of dynamic risk measures

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

    In this paper we discuss time consistency of risk averse multistage stochastic programming problems. We show, in a framework of finite scenario trees, that composition of law invariant coherent risk measures can be law invariant only for the expectation or max-risk measures. CitationPreprintArticleDownload View PDF

    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

    Optimizing Trading Decisions for Hydro Storage Systems using Approximate Dual Dynamic Programming

  • Nils Löhndorf
  • David Wozabal
  • Stefan Minner
    • Categories Applications - OR and Management Sciences, Dynamic Programming, Stochastic Programming Tags , , ,

    We propose a new approach to optimize operations of hydro storage systems with multiple connected reservoirs which participate in wholesale electricity markets. Our formulation integrates short-term intraday with long-term interday decisions. The intraday problem considers bidding decisions as well as storage operation during the day and is formulated as a stochastic program. The interday problem … Read more

    On the Geometry of Acceptability Functionals

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

    Abstract In this paper we discuss continuity properties of acceptability functionals or risk measures. The dependence of the random variable is investigated first. The main contribution and focus of this paper is to study how acceptability functionals vary whenever the underlying probability measure is perturbed. Abstract It turns out that the Wasserstein distance provides a … Read more

    Time-inconsistent multistage stochastic programs: martingale bounds

  • Georg Ch. Pflug
  • Alois Pichler
    • Categories Dynamic Programming, Stochastic Programming Tags , ,

    Abstract. It is well known that multistage programs, which maximize expectation or expected utility, allow a dynamic programming formulation, and that other objectives destroy the dynamic programming character of the problem. This paper considers a risk measure at the final stage of a multistage stochastic program. Although these problems are not time consistent, it is … Read more

    Robust inversion, dimensionality reduction, and randomized sampling

  • Aleksandr Y. Aravkin
  • Michael P. Friedlander
  • Felix Herrmann
  • Tristan van Leeuwen
    • Categories Basic Sciences Applications, Nonlinear Optimization, Stochastic Programming Tags , , ,

    We consider a class of inverse problems in which the forward model is the solution operator to linear ODEs or PDEs. This class admits several dimensionality-reduction techniques based on data averaging or sampling, which are especially useful for large-scale problems. We survey these approaches and their connection to stochastic optimization. The data-averaging approach is only … Read more

    Robustifying Convex Risk Measures: A Non-Parametric Approach

  • David Wozabal
    • Categories Finance and Economics, Robust Optimization, Stochastic Programming

    We introduce a framework for robustifying portfolio selection problems with respect to ambiguity in the distribution of the random asset losses. In particular, we are interested in convex, version independent risk measures. To robustify these risk measures, we use an ambiguity set which is defined as a neighborhood around a reference probability measure which represents … Read more