stochastic optimization

Convergence of stochastic average approximation for stochastic optimization problems with mixed expectation and per-scenario constraints

  • Mihai Anitescu
  • Birge John
    • Categories Constrained Nonlinear Optimization, Stochastic Programming Tags , ,

    We present a framework for ensuring convergence of sample average approximations to stochastic optimization problems that include expectation constraints in addition to per-scenario constraints. Citation Preprint ANL/MCS 1562-1108 Article Download View Convergence of stochastic average approximation for stochastic optimization problems with mixed expectation and per-scenario constraints

    An information-based approximation scheme for stochastic optimization problems in continuous time

  • Daniel Kuhn
    • Categories Infinite Dimensional Optimization, Stochastic Programming Tags , , , ,

    Dynamic stochastic optimization problems with a large (possibly infinite) number of decision stages and high-dimensional state vector are inherently difficult to solve. In fact, scenario tree based algorithms are unsuitable for problems with many stages, while dynamic programming type techniques are unsuitable for problems with many state variables. This article proposes a stage aggregation scheme … Read more

    Formulation and solution strategies for nonparametric nonlinear stochastic programs, with an application in finance

  • Fabian Bastin
  • Philippe L. Toint
  • Cinzia Cirillo
    • Categories Finance and Economics, Nonlinear Optimization, Stochastic Programming Tags , , ,

    We consider a class of stochastic programming models where the uncertainty is classically represented using parametric distributions families. The parameters are then usually estimated together with the optimal value of the problem. However, misspecification of the underlying random variables often leads to irrealistic results when little is known about their true distributions. We propose to … Read more

    On Rates of Convergence for Stochastic Optimization Problems Under Non-I.I.D. Sampling

  • Tito Homem-de-Mello
    • Categories Optimization of Simulated Systems, Stochastic Programming Tags , , , , , ,

    In this paper we discuss the issue of solving stochastic optimization problems by means of sample average approximations. Our focus is on rates of convergence of estimators of optimal solutions and optimal values with respect to the sample size. This is a well-studied problem in case the samples are independent and identically distributed (i.e., when … Read more

    Solving the Vehicle Routing Problem with Stochastic Demands using the Cross Entropy Method

  • Krishna Chepuri
  • Tito Homem-de-Mello
    • Categories Applications - OR and Management Sciences, Global Optimization Tags , ,

    An alternate formulation of the classical vehicle routing problem with stochastic demands (VRPSD)is considered. We propose a new heuristic method to solve the problem. The algorithm is a modified version of the so-called Cross-Entropy method, which has been proposed in the literature as a heuristics for deterministic combinatorial optimization problems based upon concepts of rare-event … Read more

    Conditional Risk Mappings

  • Andrzej Ruszczyński
  • Alexander Shapiro
    • Categories Finance and Economics, Stochastic Programming Tags , , , , ,

    We introduce an axiomatic definition of a conditional convex risk mapping and we derive its properties. In particular, we prove a representation theorem for conditional risk mappings in terms of conditional expectations. We also develop dynamic programming relations for multistage optimization problems involving conditional risk mappings. Citation Preprint Article Download View Conditional Risk Mappings

    Optimization of Convex Risk Functions

  • Andrzej Ruszczyński
  • Alexander Shapiro
    • Categories Finance and Economics, Stochastic Programming Tags , , , ,

    We consider optimization problems involving convex risk functions. By employing techniques of convex analysis and optimization theory in vector spaces of measurable functions we develop new representation theorems for risk models, and optimality and duality theory for problems involving risk functions. Citation Preprint Article Download View Optimization of Convex Risk Functions