Stochastic Programming

A Data Efficient and Feasible Level Set Method for Stochastic Convex Optimization with Expectation Constraints

  • Qihang Lin
  • Selvaprabu Nadarajah
  • Negar Soheili
  • Tianbao Yang
    • Categories Convex Optimization, Stochastic Programming Tags , , ,

    Stochastic convex optimization problems with expectation constraints (SOECs) are encountered in statistics and machine learning, business, and engineering. In data-rich environments, the SOEC objective and constraints contain expectations defined with respect to large datasets. Therefore, efficient algorithms for solving such SOECs need to limit the fraction of data points that they use, which we refer … Read more

    Robust stochastic optimization with the proximal point method

  • Damek Davis
  • Dmitriy Drusvyatskiy
    • Categories Convex Optimization, Stochastic Programming Tags , , , ,

    Standard results in stochastic convex optimization bound the number of samples that an algorithm needs to generate a point with small function value in expectation. In this work, we show that a wide class of such algorithms on strongly convex problems can be augmented with sub-exponential confidence bounds at an overhead cost that is only … Read more

    Logic-based Benders Decomposition and Binary Decision Diagram Based Approaches for Stochastic Distributed Operating Room Scheduling

  • Dionne M. Aleman
  • Merve Bodur
  • Cheng Guo
  • David R. Urbach
    • Categories Cutting Plane Approaches, Scheduling, Stochastic Programming

    The distributed operating room (OR) scheduling problem aims to find an assignment of surgeries to ORs across collaborating hospitals that share their waiting lists and ORs. We propose a stochastic extension of this problem where surgery durations are considered to be uncertain. In order to obtain solutions for the challenging stochastic model, we use sample … Read more

    A conservative convergent solution for continuously distributed two-stage stochastic optimization problems

  • Carlos Gamboa
  • Alexandre Street
  • Davi Valladão
    • Categories Stochastic Programming Tags , ,

    Two-stage stochastic programming is a mathematical framework widely used in real- life applications such as power system operation planning, supply chains, logistics, inventory management, and financial planning. Since most of these problems cannot be solved analytically, decision makers make use of numerical methods to obtain a near-optimal solution. Some applica- tions rely on the implementation … Read more

    Mixed Integer Programming models for planning maintenance at offshore wind farms under uncertainty

  • Albert H. Schrotenboer
  • Evrim Ursavas
  • Iris F. A. Vis
    • Categories (Mixed) Integer Linear Programming, Stochastic Programming, Transportation Tags , , , , ,

    We introduce the Stochastic Maintenance Fleet Transportation Problem for Offshore wind farms (SMFTPO), in which a maintenance provider determines an optimal, medium-term planning for maintaining multiple wind farms while controlling for uncertainty in the maintenance tasks and weather conditions. Since the maintenance provider is typically not the owner of a wind farm, it needs to … Read more

    Distributionally robust chance constrained geometric optimization

  • Jia Liu
  • Abdel Lisser
  • Zhiping Chen
    • Categories Convex Optimization, Robust Optimization, Stochastic Programming Tags , , ,

    This paper discusses distributionally robust geometric programs with individual and joint chance constraints. Seven groups of uncertainty sets are considered: uncertainty sets with first two order moments information, uncertainty sets constrained by the Kullback-Leibler divergence distance with a normal reference distribution or a discrete reference distribution, uncertainty sets with known first moments or known first … Read more

    Tight tail probability bounds for distribution-free decision making

  • Ruud C.M. Brekelmans
  • Dick den Hertog
  • Wouter Van Eekelen
  • Ernst Roos
  • Johan Van Leeuwaarden
    • Categories Robust Optimization, Stochastic Programming Tags , , ,

    Chebyshev’s inequality provides an upper bound on the tail probability of a random variable based on its mean and variance. While tight, the inequality has been criticized for only being attained by pathological distributions that abuse the unboundedness of the underlying support and are not considered realistic in many applications. We provide alternative tight lower … Read more

    The stochastic multi-gradient algorithm for multi-objective optimization and its application to supervised machine learning

  • Suyun Liu
  • Luis Nunes Vicente
    • Categories Convex Optimization, Multi-Criteria Optimization, Stochastic Programming Tags , , ,

    Optimization of conflicting functions is of paramount importance in decision making, and real world applications frequently involve data that is uncertain or unknown, resulting in multi-objective optimization (MOO) problems of stochastic type. We study the stochastic multi-gradient (SMG) method, seen as an extension of the classical stochastic gradient method for single-objective optimization. At each iteration … Read more

    Data-Driven Distributionally Robust Appointment Scheduling over Wasserstein Balls

  • Ruiwei Jiang
  • Minseok Ryu
  • Guanglin Xu
    • Categories Robust Optimization, Scheduling, Stochastic Programming

    We study a single-server appointment scheduling problem with a fixed sequence of appointments, for which we must determine the arrival time for each appointment. We specifically examine two stochastic models. In the first model, we assume that all appointees show up at the scheduled arrival times yet their service durations are random. In the second … Read more

    A Stochastic Bin Packing Approach for Server Consolidation with Conflicts

  • Waltenegus Dargie
  • John Martinovic
  • Markus Hähnel
  • Guntram Scheithauer
    • Categories 0-1 Programming, Applications - Science and Engineering, Stochastic Programming Tags , ,

    The energy consumption of large-scale data centers or server clusters is expected to grow significantly in the next couple of years contributing to up to 13 percent of the worlwide energy demand in 2030. As the involved processing units require a disproportional amount of energy when they are idle, underutilized or overloaded, balancing the supply … Read more