Stochastic Programming

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

    On vehicle routing problems with stochastic demands — Scenario-optimal recourse policies

  • Matheus Jun Ota
  • Ricardo Fukasawa
    • Categories Branch and Cut Algorithms, Stochastic Programming, Transportation Tags , ,

    Two-Stage Vehicle Routing Problems with Stochastic Demands (VRPSDs) form a class of stochastic combinatorial optimization problems where routes are planned in advance, demands are revealed upon vehicle arrival, and recourse actions are triggered whenever capacity is exceeded. Following recent works, we consider VRPSDs where demands are given by an empirical probability distribution of scenarios. Existing … Read more

    An objective-function-free algorithm for nonconvex stochastic optimization with deterministic equality and inequality constraints

  • Serge Gratton
  • Philippe L. Toint
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization, Stochastic Programming Tags , , , ,

    An algorithm is proposed for solving optimization problems with stochastic objective and deterministic equality and inequality constraints. This algorithm is objective-function-free in the sense that it only uses the objective’s gradient and never evaluates the function value. It is based on an adaptive selection of function-decreasing and constraint-improving iterations, the first ones using an Adagrad-type … Read more

    Globalized Adversarial Regret Optimization: Robust Decisions with Uncalibrated Predictions

  • Jannis Kurtz
  • Bart Paul Gerard van Parys
    • Categories Robust Optimization, Stochastic Programming Tags , ,

    Optimization problems routinely depend on uncertain parameters that must be predicted before a decision is made. Classical robust and regret formulations are designed to handle erroneous predictions and can provide statistical error bounds in simple settings. However, when predictions lack rigorous error bounds (as is typical of modern machine learning methods) classical robust models often … Read more

    Zeroth-Order Methods for Nonconvex-Strongly Concave Stochastic Minimax Problems with Decision-Dependent Distributions

  • Zili Luo
  • Yongchao Liu
    • Categories Nonlinear Optimization, Optimization in Data Science, Stochastic Programming Tags , , , ,

    Stochastic minimax problems with decision-dependent distributions (SMDD) have emerged as a crucial framework for modeling complex systems where data distributions drift in response to decision variables. Most existing methods for SMDD rely on an explicit functional relationship between the decision variables and the probability distribution. In this paper, we propose two sample-based zeroth-order algorithms, namely … Read more

    Data-driven Policies For Two-stage Stochastic Linear Programs

  • Chhavi Sharma
  • Harsha Gangammanavar
    • Categories Linear Programming, Optimization in Data Science, Stochastic Programming Tags , , ,

    A stochastic program typically involves several parameters, including deterministic first-stage parameters and stochastic second-stage elements that serve as input data. These programs are re-solved whenever any input parameter changes. However, in practical applications, quick decision-making is necessary, and solving a stochastic program from scratch for every change in input data can be computationally costly. This … Read more

    Solving Chance Constrained Programs via a Penalty based Difference of Convex Approach

  • Zhiping Li
  • Nan Jiang
  • Rujun Jiang
    • Categories Nonlinear Optimization, Stochastic Programming Tags , , ,

    We develop two penalty based difference of convex (DC) algorithms for solving chance constrained programs. First, leveraging a rank-based DC decomposition of the chance constraint, we propose a proximal penalty based DC algorithm in the primal space that does not require a feasible initialization. Second, to improve numerical stability in the general nonlinear settings, we … Read more

    Chance-Constrained Linear Complementarity Problems

  • RenĂ© Henrion
  • Martin Schmidt
    • Categories Complementarity and Variational Inequalities, Energy, Stochastic Programming Tags , , , , ,

    We study linear complementarity problems (LCPs) under uncertainty, which we model using chance constraints. Since the complementarity condition of the LCP is an equality constraint, it is required to consider relaxations, which naturally leads to optimization problems in which the relaxation parameters are minimized for given probability levels. We focus on these optimization problems and … Read more