Stochastic Programming

A Dynamic Strategic Plan for the Transition to a Clean Bus Fleet using Multi-Stage Stochastic Programming with a Case Study in Istanbul

  • Neman Karimi
  • Burak Kocuk
  • Tuğçe Yüksel
    • Categories Energy, Stochastic Programming, Transportation Tags , , ,

    In recent years, the transition to clean bus fleets has accelerated. Although this transition might bring environmental and economic benefits, it requires a long-term strategic plan due to the large investment costs involved. This paper proposes a multi-stage stochastic program to optimize strategic plans for the clean bus fleet transition that explicitly considers the uncertainty … Read more

    Variance-reduced first-order methods for deterministically constrained stochastic nonconvex optimization with strong convergence guarantees

  • Zhaosong Lu
  • Sanyou Mei
  • Yifeng Xiao
    • Categories Constrained Nonlinear Optimization, Stochastic Programming Tags , , , , ,

    \(\) In this paper, we study a class of deterministically constrained stochastic optimization problems. Existing methods typically aim to find an \(\epsilon\)-stochastic stationary point, where the expected violations of both constraints and first-order stationarity are within a prescribed accuracy \(\epsilon\). However, in many practical applications, it is crucial that the constraints be nearly satisfied with … Read more

    Estimating the Unobservable Components of Electricity Demand Response with Inverse Optimization

  • Adrian Esteban Perez
    • Categories Energy, Statistics, Stochastic Programming Tags , , , , ,

    Understanding and predicting the electricity demand responses to prices are critical activities for system operators, retailers, and regulators. While conventional machine learning and time series analyses have been adequate for the routine demand patterns that have adapted only slowly over many years, the emergence of active consumers with flexible assets such as solar-plus-storage systems, and … Read more

    Probabilistic Iterative Hard Thresholding for Sparse Learning

  • Matteo Bergamaschi
  • Andrea Cristofari
  • Vyacheslav Kungurtsev
  • Francesco Rinaldi
    • Categories Nonlinear Optimization, Stochastic Programming Tags , ,

    For statistical modeling wherein the data regime is unfavorable in terms of dimensionality relative to the sample size, finding hidden sparsity in the ground truth can be critical in formulating an accurate statistical model. The so-called “l0 norm”, which counts the number of non-zero components in a vector, is a strong reliable mechanism of enforcing … Read more

    A Two Stepsize SQP Method for Nonlinear Equality Constrained Stochastic Optimization

  • Michael J. O'Neill
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization, Stochastic Programming Tags , , , ,

    We develop a Sequential Quadratic Optimization (SQP) algorithm for minimizing a stochastic objective function subject to deterministic equality constraints. The method utilizes two different stepsizes, one which exclusively scales the component of the step corrupted by the variance of the stochastic gradient estimates and a second which scales the entire step. We prove that this … Read more

    A Markovian Model for Learning-to-Optimize

  • Michael Sucker
  • Peter Ochs
    • Categories Optimization in Data Science, Stochastic Approaches, Stochastic Programming Tags , , , ,

    We present a probabilistic model for stochastic iterative algorithms with the use case of optimization algorithms in mind. Based on this model, we present PAC-Bayesian generalization bounds for functions that are defined on the trajectory of the learned algorithm, for example, the expected (non-asymptotic) convergence rate and the expected time to reach the stopping criterion. … Read more

    Probing-Enhanced Stochastic Programming

  • Zhichao Ma
  • Youngdae Kim
  • Jeff Linderoth
  • James R. Luedtke
  • Logan Matthews
    • Categories Stochastic Programming Tags , , ,

    \(\) We consider a two-stage stochastic decision problem where the decision-maker has the opportunity to obtain information about the distribution of the random variables $\xi$ that appear in the problem through a set of discrete actions that we refer to as probing. Probing components of a random vector $\eta$ that is jointly-distributed with $\xi$ allows … Read more

    The Blessing of Strategic Customers in Personalized Pricing

  • Zhi Chen
  • Bradley Sturt
  • Weijun Xie
    • Categories Infinite Dimensional Optimization, Robust Optimization, Stochastic Programming

    We consider a feature-based personalized pricing problem in which the buyer is strategic: given the seller’s pricing policy, the buyer can augment the features that they reveal to the seller to obtain a low price for the product. We model the seller’s pricing problem as a stochastic program over an infinite-dimensional space of pricing policies … Read more

    Properties of Two-Stage Stochastic Multi-Objective Linear Programs

  • Akshita Gupta
  • Susan R. Hunter
    • Categories Multi-Criteria Optimization, Other Topics, Stochastic Programming Tags , ,

    We consider a two-stage stochastic multi-objective linear program (TSSMOLP) which is a natural multi-objective generalization of the well-studied two-stage stochastic linear program. The second-stage recourse decision is governed by an uncertain multi-objective linear program whose solution maps to an uncertain second-stage nondominated set. The TSSMOLP then comprises the objective function, which is the Minkowsi sum … Read more