Convergence Analysis and a DC Approximation Method for Data-driven Mathematical Programs with Distributionally Robust Chance Constraints

  • Hailin Sun
  • Chen Yannan
  • Dali Zhang
    • Categories Robust Optimization, Stochastic Programming Tags , , , ,

    In this paper, we consider the convergence analysis of data-driven mathematical programs with distributionally robust chance constraints (MPDRCC) under weaker conditions without continuity assumption of distributionally robust probability functions. Moreover, combining with the data-driven approximation, we propose a DC approximation method to MPDRCC without some special tractable structures. We also give the convergence analysis of … Read more

    A Framework for Mathematical Optimization in Microservice Architectures

  • Andrea Cassioli
  • Stefan Guericke
    • Categories Applications - OR and Management Sciences, Optimization Software and Modeling Systems, Optimization Software Design Principles Tags , ,

    In the last years, the gap between solution methods in literature and optimization running in production has increased. Agile development practices, DevOps and modern cloud-based infrastructure call for a revisit of how optimization software is developed. We review the state-of-the-art, propose a development framework that can be applied across different programming languages and modeling frameworks … Read more

    Optimization and Validation of Pumping System Design and Operation for Water Supply in High-Rise Buildings

  • Lena C. Altherr
  • Peter F. Pelz
  • Philipp Leise
  • Imke-Sophie Lorenz
  • Tim M. Müller
    • Categories Global Optimization Applications, Mechanical Engineering Tags , , , , ,

    The application of mathematical optimization methods provides the capacity to increase the energy efficiency and to lower the investment costs of technical systems, considerably. We present a system approach for the optimization of the design and operation of pumping systems and exemplify it by applying it to the water supply of high-rise buildings. The underlying … Read more

    Supermodularity in Two-Stage Distributionally Robust Optimization

  • Daniel Zhuoyu Long
  • Jin Qi
  • Aiqi Zhang
    • Categories Applications - OR and Management Sciences, Linear Programming, Robust Optimization

    In this paper, we solve a class of two-stage distributionally robust optimization problems which have the property of supermodularity. We exploit the explicit upper bounds on the expectation of supermodular functions and derive the worst-case distribution for the robust counterpart. This enables us to develop an efficient method to derive an exact optimal solution of … Read more

    Exploiting Aggregate Sparsity in Second Order Cone Relaxations for Quadratic Constrained Quadratic Programming Problems

  • Heejune Sheen
  • Makoto Yamashita
    • Categories Quadratic Programming, Second-Order Cone Programming, Semi-definite Programming Tags , , , ,

    Among many approaches to increase the computational efficiency of semidefinite programming (SDP) relaxation for quadratic constrained quadratic programming problems (QCQPs), exploiting the aggregate sparsity of the data matrices in the SDP by Fukuda et al. (2001) and second-order cone programming (SOCP) relaxation have been popular. In this paper, we exploit the aggregate sparsity of SOCP … Read more

    Persistency of Linear Programming Formulations for the Stable Set Problem

  • Elisabeth Rodriguez-Heck
  • Matthias Walter
  • Karl Stickler
  • Stefan Weltge
    • Categories 0-1 Programming, Polyhedra Tags , ,

    The Nemhauser-Trotter theorem states that the standard linear programming (LP) formulation for the stable set problem has a remarkable property, also known as (weak) persistency: for every optimal LP solution that assigns integer values to some variables, there exists an optimal integer solution in which these variables retain the same values. While the standard LP … Read more

    Understanding Limitation of Two Symmetrized Orders by Worst-case Complexity

  • Ruoyu Sun
  • Zhisheng Xiao
  • Peijun Xiao
    • Categories Complementarity and Variational Inequalities, Convex and Nonsmooth Optimization, Nonlinear Optimization Tags , , ,

    It was recently found that the standard version of multi-block cyclic ADMM diverges. Interestingly, Gaussian Back Substitution ADMM (GBS-ADMM) and symmetric Gauss-Seidel ADMM (sGS-ADMM) do not have the divergence issue. Therefore, it seems that symmetrization can improve the performance of the classical cyclic order. In another recent work, cyclic CD (Coordinate Descent) was shown to … Read more

    Minimizing Airplane Boarding Time

  • Andreas M. Tillmann
  • Felix J. L. Willamowski
    • Categories Applications - OR and Management Sciences, Combinatorial Optimization Tags , ,

    The time it takes passengers to board an airplane is known to influence the turn-around time of the aircraft and thus bears a significant cost-saving potential for airlines. Although minimizing boarding time therefore is the most important goal from an economic perspective, previous efforts to design efficient boarding strategies apparently never tackled this task directly. … Read more

    Exact Methods for the Traveling Salesman Problem with Drone

  • Roberto Roberti
  • Mario Ruthmair
    • Categories (Mixed) Integer Linear Programming, Dynamic Programming, Transportation Tags , , , ,

    Efficiently handling last-mile deliveries becomes more and more important nowadays. Using drones to support classical vehicles allows improving delivery schedules as long as efficient solution methods to plan last-mile deliveries with drones are available. We study exact solution approaches for some variants of the traveling salesman problem with drone (TSP-D) in which a truck and … Read more

    A Polynomial-time Algorithm with Tight Error Bounds for Single-period Unit Commitment Problem

  • S.C. Fang
  • Ruotian Gao
  • Wenxun Xing
  • Cheng Lu
    • Categories (Mixed) Integer Nonlinear Programming, Approximation Algorithms, Scheduling Tags , , , ,

    This paper proposes a Lagrangian dual based polynomial-time approximation algorithm for solving the single-period unit commitment problem, which can be formulated as a mixed integer quadratic programming problem and proven to be NP-hard. Tight theoretical bounds for the absolute errors and relative errors of the approximate solutions generated by the proposed algorithm are provided. Computational … Read more