Stochastic Programming

A Review on the Performance of Linear and Mixed Integer Two-Stage Stochastic Programming Algorithms and Software

  • Robert Apap
  • Ignacio E. Grossmann
  • Can Li
  • Juan Torres
    • Categories (Mixed) Integer Linear Programming, Stochastic Programming Tags

    This paper presents a tutorial on the state-of-the-art methodologies for the solution of two-stage (mixed-integer) linear stochastic programs and provides a list of software designed for this purpose. The methodologies are classifi ed according to the decomposition alternatives and the types of the variables in the problem. We review the fundamentals of Benders Decomposition, Dual Decomposition … Read more

    Relating Single-Scenario Facets to the Convex Hull of the Extensive Form of a Stochastic Single-Node Flow Polytope

  • Victor A. Gonzalez
  • Andrew J. Schaefer
  • Mehdi Hemmati
  • David T. Mildebrath
    • Categories (Mixed) Integer Linear Programming, Polyhedra, Stochastic Programming Tags , ,

    Stochastic mixed-integer programs (SMIPs) are a widely-used modeling paradigm for sequential decision making under uncertainty. One popular solution approach to solving SMIPs is to solve the so-called “extensive form” directly as a large-scale (deterministic) mixed-integer program. In this work, we consider the question of when a facet-defining inequality for the convex hull of a deterministic, … Read more

    Portfolio Optimization with Irreversible Long-Term Investments in Renewable Energy under Policy Risk: A Mixed-Integer Multistage Stochastic Model and a Moving-Horizon Approach

  • Nadine Gatzert
  • Martin Schmidt
  • Alexander Martin
  • Benjamin Seith
  • Nikolai Vogl
    • Categories (Mixed) Integer Linear Programming, Applications - OR and Management Sciences, Stochastic Programming Tags , , , ,

    Portfolio optimization is an ongoing hot topic of mathematical optimization and management science. Due to the current financial market environment with low interest rates and volatile stock markets, it is getting more and more important to extend portfolio optimization models by other types of investments than classical assets. In this paper, we present a mixed-integer … Read more

    Benders Cut Classification via Support Vector Machines for Solving Two-stage Stochastic Programs

  • Huiwen Jia
  • Siqian Shen
    • Categories Cutting Plane Approaches, Stochastic Programming Tags , , ,

    We consider Benders decomposition for solving two-stage stochastic programs with complete recourse based on finite samples of the uncertain parameters. We define the Benders cuts binding at the final optimal solution or the ones significantly improving bounds over iterations as valuable cuts. We propose a learning-enhanced Benders decomposition (LearnBD) algorithm, which adds a cut classification … Read more

    Adaptive Two-stage Stochastic Programming with an Application to Capacity Expansion Planning

  • Shabbir Ahmed
  • Nagi Gebraeel
  • Beste Basciftci
    • Categories Applications - OR and Management Sciences, Stochastic Programming Tags , , , , ,

    Multi-stage stochastic programming is a well-established framework for sequential decision making under uncertainty by seeking policies that are fully adapted to the uncertainty. Often, e.g. due to contractual constraints, such flexible and adaptive policies are not desirable, and the decision maker may need to commit to a set of actions for a certain number of … Read more

    Confidence Regions in Wasserstein Distributionally Robust Estimation

  • Jose Blanchet
  • Karthyek Murthy
  • Nian Si
    • Categories Robust Optimization, Stochastic Programming Tags , , ,

    Wasserstein distributionally robust optimization (DRO) estimators are obtained as solutions of min-max problems in which the statistician selects a parameter minimizing the worst-case loss among all probability models within a certain distance (in a Wasserstein sense) from the underlying empirical measure. While motivated by the need to identify model parameters (or) decision choices that are … Read more

    Sharing the Value-at-Risk under Distributional Ambiguity

  • Weijun Xie
  • Zhi Chen
    • Categories Applications - OR and Management Sciences, Robust Optimization, Stochastic Programming Tags , , ,

    This paper considers the problem of risk sharing, where a coalition of homogeneous agents, each bearing a random cost, aggregates their costs and shares the value-at-risk of such a risky position. Due to limited distributional information in practice, the joint distribution of agents’ random costs is difficult to acquire. The coalition, being aware of the … Read more

    Risk Guarantees for End-to-End Prediction and Optimization Processes

  • Nam Ho-Nguyen
  • Fatma Kılınç-Karzan
    • Categories Robust Optimization, Stochastic Programming

    Prediction models are often employed in estimating parameters of optimization models. Despite the fact that in an \emph{end-to-end} view, the real goal is to achieve good optimization performance, the prediction performance is measured on its own. While it is usually believed that good prediction performance in estimating the parameters will result in good subsequent optimization … Read more

    Risk-Averse Bi-Level Stochastic Network Interdiction Model for Cyber-Security Risk Management

  • Tanveer Hossain Bhuiyan
  • Mahantesh Halappanavar
  • Hugh R. Medal
  • Apurba Nandi
    • Categories (Mixed) Integer Linear Programming, Network Optimization, Stochastic Programming Tags , , , ,

    Security of cyber networks is crucial; recent severe cyber-attacks have had a devastating effect on many large organizations. The attack graph, which maps the potential attack paths of a cyber network, is a popular tool for analyzing cyber system vulnerability. In this study, we propose a bi-level stochastic network interdiction model on an attack graph … Read more

    Hybrid Stochastic Gradient Descent Algorithms forStochastic Nonconvex Optimization

  • M. Lam Nguyen
  • Quoc Tran-Dinh
  • H. Nhan Pham
  • T. Dzung Phan
    • Categories Nonlinear Optimization, Stochastic Programming

    We introduce a hybrid stochastic estimator to design stochastic gradient algorithms for solving stochastic optimization problems. Such a hybrid estimator is a convex combination of two existing biased and unbiased estimators and leads to some useful property on its variance. We limit our consideration to a hybrid SARAH-SGD for nonconvex expectation problems. However, our idea … Read more