stochastic programming

A progressive decoupling algorithm for minimizing the difference of convex and weakly convex functions over a linear subspace

  • Welington de Oliveira
  • João Carlos Souza
    • Categories Nonlinear Optimization, Nonsmooth Optimization Tags , ,

    Commonly, decomposition and splitting techniques for optimization problems strongly depend on convexity. Implementable splitting methods for nonconvex and nonsmooth optimization problems are scarce and often lack convergence guarantees. Among the few exceptions is the Progressive Decoupling Algorithm (PDA), which has local convergence should convexity be elicitable. In this work, we furnish PDA with a descent … Read more

    Benders decomposition with scaled cuts for multistage stochastic mixed-integer programs

  • Ward Romeijnders
  • Niels van der Laan
    • Categories Stochastic Programming Tags , ,

    We consider Benders decomposition algorithms for multistage stochastic mixed-integer programs (SMIPs) with general mixed-integer decision variables at every node in the scenario tree. We derive a hierarchy of convex polyhedral lower bounds for the value functions and expected cost to-go functions in multistage SMIPs using affine parametric cutting planes in extended spaces for the feasible … Read more

    Exploiting Overlap Information in Chance-constrained Program with Random Right-hand Side

  • Wei Lv
  • Wei-Kun Chen
  • Yu-Hong Dai
  • Xiao-Jiao Tong
    • Categories (Mixed) Integer Linear Programming, Stochastic Programming Tags , , , ,

    We consider the chance-constrained program (CCP) with random right-hand side under a finite discrete distribution. It is known that the standard mixed integer linear programming (MILP) reformulation of the CCP is generally difficult to solve by general-purpose solvers as the branch-and-cut search trees are enormously large, partly due to the weak linear programming relaxation. In … Read more

    Applying random coordinate descent in a probability maximization scheme

  • Edit Csizmás
  • Rajmund Drenyovszki
  • Tamas Szantai
  • Csaba I. Fábián
    • Categories Stochastic Programming Tags , ,

    Gradient computation of multivariate distribution functions calls for considerable effort. A standard procedure is component-wise computation, hence coordinate descent is an attractive choice. This paper deals with constrained convex problems. We apply random coordinate descent in an approximation scheme that is an inexact cutting-plane method from a dual viewpoint. We present convergence proofs and a … Read more

    Distributionally Fair Stochastic Optimization using Wasserstein Distance

  • Ye Qing
  • Grani A. Hanasusanto
  • Weijun Xie
    • Categories Stochastic Programming Tags , ,

    A traditional stochastic program under a finite population typically seeks to optimize efficiency by maximizing the expected profits or minimizing the expected costs, subject to a set of constraints. However, implementing such optimization-based decisions can have varying impacts on individuals, and when assessed using the individuals’ utility functions, these impacts may differ substantially across demographic … Read more

    Active Set-based Inexact Proximal Bundle Algorithm for Stochastic Quadratic Programming

  • Niloofar Fadavi
  • Harsha Gangammanavar
    • Categories Convex Optimization, Stochastic Programming Tags , , , ,

    In this paper, we examine two-stage stochastic quadratic programming problems, where the objective function of the first and second stages are quadratic functions, and the constraints are linear. The uncertainty is associated with the second-stage right-hand side and variable bounds. In large-scale settings, when the number of scenarios necessary to represent the underlying stochastic process … Read more

    A hybrid branch-and-bound and interior-point algorithm for stochastic mixed-integer nonlinear second-order cone programming

  • Baha Alzalg
    • Categories (Mixed) Integer Nonlinear Programming, Cutting Plane Approaches, Second-Order Cone Programming Tags , , , ,

    One of the chief attractions of stochastic mixed-integer second-order cone programming is its diverse applications, especially in engineering (Alzalg and Alioui, {\em IEEE Access}, 10:3522-3547, 2022). The linear and nonlinear versions of this class of optimization problems are still unsolved yet. In this paper, we develop a hybrid optimization algorithm coupling branch-and-bound and primal-dual interior-point … Read more

    Distributions and Bootstrap for Data-based Stochastic Programming

  • Xiaotie Chen
  • David L. Woodruff
    • Categories Stochastic Programming Tags , , ,

    In the context of optimization under uncertainty, we consider various combinations of distribution estimation and resampling (bootstrap and bagging) for obtaining samples used to acquire a solution and for computing a confidence interval for an optimality gap. This paper makes three experimental contributions to on-going research in data driven stochastic programming: a) most of the … Read more

    Enhancing explainability of stochastic programming solutions via scenario and recourse reduction

  • Tushar Rathi
  • Rishabh Gupta
  • Jose M. Pinto
  • Qi Zhang
    • Categories Stochastic Programming Tags , , ,

    Stochastic programming (SP) is a well-studied framework for modeling optimization problems under uncertainty. However, despite the significant advancements in solving large SP models, they are not widely used in industrial practice, often because SP solutions are difficult to understand and hence not trusted by the user. Unlike deterministic optimization models, SP models generally involve recourse … Read more

    End-to-End Learning for Stochastic Optimization: A Bayesian Perspective

  • Yves Rychener
  • Daniel Kuhn
  • Tobias Sutter
    • Categories Stochastic Programming Tags , , ,

    We develop a principled approach to end-to-end learning in stochastic optimization. First, we show that the standard end-to-end learning algorithm admits a Bayesian interpretation and trains a posterior Bayes action map. Building on the insights of this analysis, we then propose new end-to-end learning algorithms for training decision maps that output solutions of empirical risk … Read more