Stochastic Programming

Worst-Case Complexity of an SQP Method for Nonlinear Equality Constrained Stochastic Optimization

  • Frank E. Curtis
  • Michael J. O'Neill
  • Daniel P. Robinson
    • Categories Constrained Nonlinear Optimization, Stochastic Programming Tags , , ,

    A worst-case complexity bound is proved for a sequential quadratic optimization (commonly known as SQP) algorithm that has been designed for solving optimization problems involving a stochastic objective function and deterministic nonlinear equality constraints. Barring additional terms that arise due to the adaptivity of the monotonically nonincreasing merit parameter sequence, the proved complexity bound is … Read more

    A Stochastic Bregman Primal-Dual Splitting Algorithm for Composite Optimization

  • Antonio Silveti-Falls
  • Cesare Molinari
  • Jalal Fadili
    • Categories Convex and Nonsmooth Optimization, Infinite Dimensional Optimization, Stochastic Programming Tags , , , , , , , ,

    We study a stochastic first order primal-dual method for solving convex-concave saddle point problems over real reflexive Banach spaces using Bregman divergences and relative smoothness assumptions, in which we allow for stochastic error in the computation of gradient terms within the algorithm. We show ergodic convergence in expectation of the Lagrangian optimality gap with a … 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

    Hub Network Design Problem with Capacity, Congestion and Stochastic Demand Considerations

  • Vedat Bayram
  • Barış Yıldız
  • M. Saleh Farham
    • Categories Second-Order Cone Programming, Stochastic Programming, Transportation Tags , , , , , , ,

    We introduce the hub network design problem with congestion, capacity, and stochastic demand considerations (HNDC), which generalizes the classical hub location problem in several directions. In particular, we extend state-of-the-art by integrating capacity acquisition decision and congestion cost effect into the problem and allowing dynamic routing for origin-destination pairs. Connecting strategic and operational level decisions, … Read more

    Mean-Covariance Robust Risk Measurement

  • Viet Anh Nguyen
  • Soroosh Shafieezadeh-Abadeh
  • Damir Filipovic
  • Daniel Kuhn
    • Categories Finance and Economics, Robust Optimization, Stochastic Programming Tags ,

    We introduce a universal framework for mean-covariance robust risk measurement and portfolio optimization. We model uncertainty in terms of the Gelbrich distance on the mean-covariance space, along with prior structural information about the population distribution. Our approach is related to the theory of optimal transport and exhibits superior statistical and computational properties than existing models. … Read more

    Risk-Averse Stochastic Optimal Control: an efficiently computable statistical upper bound

  • Vincent Guigues
  • Alexander Shapiro
  • Yi Cheng
    • Categories Stochastic Programming Tags , , , , ,

    In this paper, we discuss an application of the SDDP type algorithm to nested risk-averse formulations of Stochastic Optimal Control (SOC) problems. We propose a construction of a statistical upper bound for the optimal value of risk-averse SOC problems. This outlines an approach to a solution of a long standing problem in that area of … Read more

    Distributionally risk-receptive and risk-averse network interdiction problems with general ambiguity set

  • Sumin Kang
  • Manish Bansal
    • Categories Nonlinear Optimization, Stochastic Programming Tags , , , ,

    We introduce generalizations of stochastic network interdiction problem with distributional ambiguity. Specifically, we consider a distributionally risk-averse (or robust) network interdiction problem (DRA-NIP) and a distributionally risk-receptive network interdiction problem (DRR-NIP) where a leader maximizes a follower’s minimal expected objective value for either the worst-case or the best-case, respectively, probability distribution belonging to ambiguity set … Read more

    Bayesian Distributionally Robust Optimization

  • Alexander Shapiro
  • Enlu Zhou
  • Yifan Lin
    • Categories Robust Optimization, Stochastic Programming

    We introduce a new framework, Bayesian Distributionally Robust Optimization (Bayesian-DRO), for data-driven stochastic optimization where the underlying distribution is unknown. Bayesian-DRO contrasts with most of the existing DRO approaches in the use of Bayesian estimation of the unknown distribution. To make computation of Bayesian updating tractable, Bayesian-DRO first assumes the underlying distribution takes a parametric … Read more

    Risk-averse Regret Minimization in Multi-stage Stochastic Programs

  • Mehran Poursoltani
  • Erick Delage
  • Angelos Georghiou
    • Categories Applications - OR and Management Sciences, Robust Optimization, Stochastic Programming Tags , , ,

    Within the context of optimization under uncertainty, a well-known alternative to minimizing expected value or the worst-case scenario consists in minimizing regret. In a multi-stage stochastic programming setting with a discrete probability distribution, we explore the idea of risk-averse regret minimization, where the benchmark policy can only benefit from foreseeing Delta steps into the future. … Read more

    A Finitely Convergent Cutting Plane, and a Bender’s Decomposition Algorithm for Mixed-Integer Convex and Two-Stage Convex Programs using Cutting Planes

  • Fengqiao Luo
  • Sanjay Mehrotra
    • Categories (Mixed) Integer Nonlinear Programming, Cutting Plane Approaches, Stochastic Programming Tags , , ,

    We consider a general mixed-integer convex program. We first develop an algorithm for solving this problem, and show its nite convergence. We then develop a finitely convergent decomposition algorithm that separates binary variables from integer and continuous variables. The integer and continuous variables are treated as second stage variables. An oracle for generating a parametric … Read more