Stochastic Programming

Mean and covariance matrix adaptive estimation for a weakly stationary process. Application in stochastic optimization.

  • Vincent Guigues
    • Categories Stochastic Programming

    We introduce an adaptive algorithm to estimate the uncertain parameter of a stochastic optimization problem. The procedure estimates the one-step-ahead means, variances and covariances of a random process in a distribution-free and multidimensional framework when these means, variances and covariances are slowly varying on a given past interval. The quality of the approximate problem obtained … Read more

    Stochastic Variational Inequalities:Residual Minimization Smoothing/Sample Average approximations

  • Xiaojun Chen
  • Roger J.B. Wets
  • Yanfang Zhang
    • Categories Complementarity and Variational Inequalities, Convex and Nonsmooth Optimization, Stochastic Programming Tags , ,

    The stochastic variational inequality (SVI) has been used widely, in engineering and economics, as an effective mathematical model for a number of equilibrium problems involving uncertain data. This paper presents a new expected residual minimization (ERM) formulation for a class of SVI. The objective of the ERM-formulation is Lipschitz continuous and semismooth which helps us … Read more

    Optimal Distributed Online Prediction using Mini-Batches

  • Ofer Dekel
  • Lin Xiao
  • Ran Gilad-Bachrach
  • Ohad Shamir
    • Categories Convex and Nonsmooth Optimization, Data-Mining, Stochastic Programming Tags , , ,

    Online prediction methods are typically presented as serial algorithms running on a single processor. However, in the age of web-scale prediction problems, it is increasingly common to encounter situations where a single processor cannot keep up with the high rate at which inputs arrive. In this work we present the distributed mini-batch algorithm, a method … Read more

    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

    Dynamic sampling algorithms for multi-stage stochastic programs with risk aversion

  • Vitor de Matos
  • Andrew B. Philpott
    • Categories Dynamic Programming, Stochastic Programming Tags , ,

    We consider the incorporation of a time-consistent coherent risk measure into a multi-stage stochastic programming model, so that the model can be solved using a SDDP-type algorithm. We describe the implementation of this algorithm, and study the solutions it gives for an application of hydro-thermal scheduling in the New Zealand electricity system. The performance of … Read more

    Time consistency and risk averse dynamic decision models: Definition, interpretation and practical consequences

  • Birgit Rudloff
  • Alexandre Street
  • Davi Valladão
    • Categories Finance and Economics, Stochastic Programming Tags , , , ,

    This paper aims at resolving a major obstacle to practical usage of time-consistent risk-averse decision models. The recursive objective function, generally used to ensure time consistency, is complex and has no clear/direct interpretation. Practitioners rather choose a simpler and more intuitive formulation, even though it may lead to a time inconsistent policy. Based on rigorous … Read more

    Time consistency and risk averse dynamic decision models: Definition, interpretation and practical consequences

  • Birgit Rudloff
  • Alexandre Street
  • Davi Valladão
    • Categories Finance and Economics, Stochastic Programming Tags , , , ,

    This paper aims at resolving a major obstacle to practical usage of time-consistent risk-averse decision models. The recursive objective function, generally used to ensure time consistency, is complex and has no clear/direct interpretation. Practitioners rather choose a simpler and more intuitive formulation, even though it may lead to a time inconsistent policy. Based on rigorous … Read more

    On the parallel solution of dense saddle-point linear systems arising in stochastic programming

  • Mihai Anitescu
  • Cosmin G. Petra
  • Miles Lubin
    • Categories Linear Programming, Parallel Algorithms, Stochastic Programming Tags , , ,

    We present a novel approach for solving dense saddle-point linear systems in a distributed-memory environment. This work is motivated by an application in stochastic optimization problems with recourse, but the proposed approach can be used for a large family of dense saddle-point systems, in particular those arising in convex programming. Although stochastic optimization problems have … Read more

    Construction of Risk-Averse Enhanced Index Funds

  • Miguel A. Lejeune
  • Gulay Samatli-Pac
    • Categories (Mixed) Integer Nonlinear Programming, Finance and Economics, Stochastic Programming Tags , , , ,

    We propose a partial replication strategy to construct risk-averse enhanced index funds. Our model takes into account the parameter estimation risk by defining the asset returns and the return covariance terms as random variables. The variance of the index fund return is forced to be below a low-risk threshold with a large probability, thereby limiting … Read more