Stochastic Programming

A momentum-based linearized augmented Lagrangian method for nonconvex constrained stochastic optimization

  • Qiankun Shi
  • Xiao Wang
  • Hao Wang
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization, Stochastic Programming Tags , , , , ,

    Nonconvex constrained stochastic optimization has emerged in many important application areas. Subject to general functional constraints it minimizes the sum of an expectation function and a nonsmooth regularizer. Main challenges arise due to the stochasticity in the random integrand and the possibly nonconvex functional constraints. To address these issues we propose a momentum-based linearized augmented … Read more

    Markov Chain-based Policies for Multi-stage Stochastic Integer Linear Programming with an Application to Disaster Relief Logistics

  • Margarita P Castro
  • Merve Bodur
  • Yongjia Song
    • Categories (Mixed) Integer Linear Programming, Stochastic Programming Tags , , , ,

    We introduce an aggregation framework to address multi-stage stochastic programs with mixed-integer state variables and continuous local variables (MSILPs). Our aggregation framework imposes additional structure to the integer state variables by leveraging the information of the underlying stochastic process, which is modeled as a Markov chain (MC). We demonstrate that the aggregated MSILP can be … Read more

    Asymptotic Consistency for Nonconvex Risk-Averse Stochastic Optimization with Infinite Dimensional Decision Spaces

  • Johannes Milz
  • Thomas Surowiec
    • Categories Optimization of Systems modeled by PDEs, Stochastic Programming, Systems governed by Differential Equations Optimization Tags , , , , , , ,

    Optimal values and solutions of empirical approximations of stochastic optimization problems can be viewed as statistical estimators of their true values. From this perspective, it is important to understand the asymptotic behavior of these estimators as the sample size goes to infinity, which is both of theoretical as well as practical interest. This area of … Read more

    A General Wasserstein Framework for Data-driven Distributionally Robust Optimization: Tractability and Applications

  • Jonathan Yu-Meng Li
  • Tiantian Mao
    • Categories Robust Optimization, Stochastic Programming Tags , ,

    Data-driven distributionally robust optimization is a recently emerging paradigm aimed at finding a solution that is driven by sample data but is protected against sampling errors. An increasingly popular approach, known as Wasserstein distributionally robust optimization (DRO), achieves this by applying the Wasserstein metric to construct a ball centred at the empirical distribution and finding … Read more

    A single cut proximal bundle method for stochastic convex composite optimization

  • Jiaming Liang
  • Vincent Guigues
  • Renato D.C. Monteiro
    • Categories Convex and Nonsmooth Optimization, Stochastic Programming Tags , , ,

    This paper considers optimization problems where the objective is the sum of a function given by an expectation and a closed convex composite function, and proposes stochastic composite proximal bundle (SCPB) methods for solving it. Complexity guarantees are established for them without requiring knowledge of parameters associated with the problem instance. Moreover, it is shown … Read more

    Routing and resource allocation in non-profit settings with equity and efficiency measures under demand uncertainty

  • Faisal Alkaabneh
  • Karmel S. Shehadeh
  • Ali Diabat
    • Categories (Mixed) Integer Linear Programming, Stochastic Programming Tags , , , ,

    Motivated by food distribution operations for non-profit organizations, we study a variant of the stochastic routing-allocation problem under demand uncertainty, in which one decides the assignment of trucks for demand nodes, the sequence of demand nodes to visit (i.e., truck route), and the allocation of food supply to each demand node. We propose three stochastic … Read more

    A Stochastic Optimization Approach to Energy-Efficient Underground Timetabling under Uncertain Dwell and Running Times

  • Patrick Gemander
  • Andreas Bärmann
  • Alexander Martin
    • Categories (Mixed) Integer Linear Programming, Stochastic Programming, Transportation Tags , , , , ,

    We consider a problem from the context of energy-efficient underground railway timetabling, in which an existing timetable draft is improved by slightly changing departure and running times. In practice, synchronization between accelerating and braking trains to utilize regenerative braking plays a major role for the energy-efficiency of a timetable. Since deviations from a planned timetable … Read more

    Robust planning of production routing problem in closed-loop supply chain of beverage glass bottles

  • Ali Borumand
  • Ahmadreza Marandi
  • Ali Nookabadi
  • Zümbül Atan
    • Categories Robust Optimization, Stochastic Programming, Supply Chain Management Tags , , , ,

    Closed-loop supply chains (CLSC) integrate forward and reverse flows of products and information. This integration helps companies to manage their supply chains better as they have more control and a broader view of the whole chain. Also, companies can have economic and environmental benefits from the returned products. Despite these advantages, managing CLSCs can be … Read more

    A Survey on Bilevel Optimization Under Uncertainty

  • Yasmine Beck
  • Ivana Ljubić
  • Martin Schmidt
    • Categories Global Optimization, Robust Optimization, Stochastic Programming Tags , , ,

    Bilevel optimization is a very active field of applied mathematics. The main reason is that bilevel optimization problems can serve as a powerful tool for modeling hierarchical decision making processes. This ability, however, also makes the resulting problems challenging to solve—both in theory and practice. Fortunately, there have been significant algorithmic advances in the field … Read more

    Planning of Container Crossdocking for an Express Shipment Service Network

  • Anton J. Kleywegt
  • Haotian Wu
    • Categories Applications - OR and Management Sciences, Stochastic Programming, Transportation Tags , , , ,

    In air transportation, container crossdocking refers to a loaded container that is transferred at an airport from an incoming flight to an outgoing flight without handling the freight on the container. It reduces handling time and handling cost relative to unloading the container and sorting the freight, and is an economical alternative if a sufficient … Read more