stochastic optimization

Complexity of an inexact stochastic SQP algorithm for equality constrained optimization

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

    In this paper, we consider nonlinear optimization problems with a stochastic objective function and deterministic equality constraints. We propose an inexact two-stepsize stochastic sequential quadratic programming (SQP) algorithm and analyze its worst-case complexity under mild assumptions. The method utilizes a step decomposition strategy and handles stochastic gradient estimates by assigning different stepsizes to different components … Read more

    Deep Learning for Sequential Decision Making under Uncertainty: Foundations, Frameworks, and Frontiers

  • I. Esra Buyuktahtakin Toy
    • Categories Data Science Algorithms, Optimization in Data Science, Stochastic Programming Tags , , , , , , , , , , ,

    Artificial intelligence (AI) is moving increasingly beyond prediction to support decisions in complex, uncertain, and dynamic environments. This shift creates a natural intersection with operations research and management sciences (OR/MS), which have long offered conceptual and methodological foundations for sequential decision-making under uncertainty. At the same time, recent advances in deep learning, including feedforward neural … Read more

    An Inexact Trust-Region Method for Structured Nonsmooth Optimization with Application to Risk-Averse Stochastic Programming

  • Drew P. Kouri
    • Categories Nonsmooth Optimization, Optimization of Systems modeled by PDEs, Stochastic Programming Tags , , , , ,

    We develop a trust-region method for efficiently minimizing the sum of a smooth function, a nonsmooth convex function, and the composition of a finite-valued support function with a smooth function. Optimization problems with this structure arise in numerous applications including risk-averse stochastic programming and subproblems for nonsmooth penalty nonlinear programming methods. Our method permits the … Read more

    AI for Enhancing Operations Research of Agriculture and Energy

  • Morteza Kimiaei
  • Anshu Kumar
  • Vyacheslav Kungurtsev
    • Categories (Mixed) Integer Linear Programming, Applications - OR and Management Sciences, Global Optimization Tags , , , , , , ,

    This paper surveys optimization problems arising in agriculture, energy systems, and water-energy coordination from an operations research perspective. These problems are commonly formulated as integer nonlinear programs, mixed-integer nonlinear programs, or combinatorial set optimization models, characterized by nonlinear physical constraints, discrete decisions, and intertemporal coupling. Such structures pose significant computational challenges in large-scale and repeated-solution … Read more

    Primal-dual resampling for solution validation in convex stochastic programming

  • Yi Chu
  • Susan R. Hunter
  • Raghu Pasupathy
    • Categories Convex Optimization, Optimization in Data Science, Stochastic Programming Tags , ,

    Suppose we wish to determine the quality of a candidate solution to a convex stochastic program in which the objective function is a statistical functional parameterized by the decision variable and known deterministic constraints may be present. Inspired by stopping criteria in primal-dual and interior-point methods, we develop cancellation theorems that characterize the convergence of … Read more

    Stronger cuts for Benders’ decomposition for stochastic Unit Commitment Problems based on interval variables

  • Azema
  • Vincent Leclère
  • Wim van Ackooij
    • Categories (Mixed) Integer Linear Programming, Energy, Stochastic Programming Tags , ,

    The Stochastic Unit Commitment (SUC) problem models the scheduling of power generation units under uncertainty, typically using a two-stage stochastic program with integer first-stage and continuous second-stage variables. We propose a new Benders decomposition approach that leverages an extended formulation based on interval variables, enabling decomposition by both unit and time interval under mild technical … Read more

    Optimal participation of energy communities in electricity markets under uncertainty. A multi-stage stochastic programming approach

  • Albert Solà Vilalta
  • Ignasi Mañé Bosch
  • F.-Javier Heredia
    • Categories Energy, Stochastic Programming Tags , , ,

    We propose a multi-stage stochastic programming model for the optimal participation of energy communities in electricity markets. The multi-stage aspect captures the different times at which variable renewable generation and electricity prices are observed. This results in large-scale optimization problem instances containing large scenario trees with 34 stages, to which scenario reduction techniques are applied. … Read more

    A Minimalist Bayesian Framework for Stochastic Optimization

  • Kaizheng Wang
    • Categories Global Optimization, Optimization in Data Science, Stochastic Programming Tags , , ,

    The Bayesian paradigm offers principled tools for sequential decision-making under uncertainty, but its reliance on a probabilistic model for all parameters can hinder the incorporation of complex structural constraints. We introduce a minimalist Bayesian framework that places a prior only on the component of interest, such as the location of the optimum. Nuisance parameters are … Read more

    A linesearch-based derivative-free method for noisy black-box problems

  • Giampaolo Liuzzi
  • Stefano Lucidi
  • Alberto De Santis
    • Categories Nonlinear Optimization, Stochastic Programming, Unconstrained Optimization Tags , ,

    In this work we consider unconstrained optimization problems. The objective function is known through a zeroth order stochastic oracle that gives an estimate of the true objective function. To solve these problems, we propose a derivativefree algorithm based on extrapolation techniques. Under reasonable assumptions we are able to prove convergence properties for the proposed algorithms. … Read more

    On the Convergence and Complexity of Proximal Gradient and Accelerated Proximal Gradient Methods under Adaptive Gradient Estimation

  • Raghu Bollapragada
  • Shagun Gupta
    • Categories Nonlinear Optimization, Optimization in Data Science, Stochastic Programming Tags , , , ,

    In this paper, we propose a proximal gradient method and an accelerated proximal gradient method for solving composite optimization problems, where the objective function is the sum of a smooth and a convex, possibly nonsmooth, function. We consider settings where the smooth component is either a finite-sum function or an expectation of a stochastic function, … Read more