Limited-memory Common-directions Method for Large-scale Optimization: Convergence, Parallelization, and Distributed Optimization

  • Ching-pei Lee
  • Po-Wei Wang
  • Chih-Jen Lin
    • Categories Parallel Algorithms, Unconstrained Optimization Tags , , ,

    In this paper, we present a limited-memory common-directions method for smooth optimization that interpolates between first- and second- order methods. At each iteration, a subspace of a limited dimension size is constructed using first-order information from previous iterations, and an ef- ficient Newton method is deployed to find an approximate minimizer within this subspace. With … Read more

    Randomized Assortment Optimization

  • Zhengchao Wang
  • Heikki Peura
  • Wolfram Wiesemann
    • Categories Robust Optimization, Yield Management

    When a firm selects an assortment of products to offer to customers, it uses a choice model to anticipate their probability of purchasing each product. In practice, the estimation of these models is subject to statistical errors, which may lead to significantly suboptimal assortment decisions. Recent work has addressed this issue using robust optimization, where … Read more

    Solving the Time Dependent Minimum Tour Duration and Delivery Man Problems with Dynamic Discretization Discovery

  • Mike Hewitt
  • Duc Minh Vu
  • Duc D. Vu
    • Categories (Mixed) Integer Linear Programming, Scheduling, Transportation Tags , , , ,

    In this paper, we present exact methods for solving the Time Dependent Minimum Duration Problem (TDMTDP) and the Time Dependent Delivery Man Problem (TD-DMP). Both methods are based on a Dynamic Discretization Discovery (DDD) approach for solving the Time Dependent Traveling Salesman Problem with Time Windows (TD-TSPTW). Unlike the TD-TSPTW, the problems we consider in … Read more

    A Modified Simplex Partition Algorithm to Test Copositivity

  • Mohammadreza Safi
  • Seyed Saeed Nabavi
  • Richard J. Caron
    • Categories Global Optimization Theory Tags , , , ,

    A real symmetric matrix $A$ is copositive if $x^\top Ax\geq 0$ for all $x\geq 0$. As $A$ is copositive if and only if it is copositive on the standard simplex, algorithms to determine copositivity, such as those in Sponsel et al. (J Glob Optim 52:537–551, 2012) and Tanaka and Yoshise (Pac J Optim 11:101–120, 2015) … Read more

    Connecting optimization with spectral analysis of tri-diagonal matrices

  • Jean-Bernard Lasserre
    • Categories Global Optimization, Global Optimization Theory, Nonlinear Optimization Tags

    We show that the global minimum (resp. maximum) of a continuous func- tion on a compact set can be approximated from above (resp. from below) by computing the smallest (rest. largest) eigenvalue of a hierarchy of (r × r) tri-diagonal matrices of increasing size. Equivalently it reduces to computing the smallest (resp. largest) root of … Read more

    Efficient Formulations and Decomposition Approaches for Power Peak Reduction in Railway Traffic via Timetabling

  • Andreas Bärmann
  • Alexander Martin
  • Oskar Schneider
    • Categories Cutting Plane Approaches, Polyhedra, Scheduling Tags , , , ,

    Over the last few years, optimization models for the energy-efficient operation of railway traffic have received more and more attention, particularly in connection with timetable design. In this work, we study the effect of load management via timetabling. The idea is to consider trains as time-flexible consumers in the railway power supply network and to … Read more

    On the Impact of Deep Learning-based Time-series Forecasts on Multistage Stochastic Programming Policies

  • Merve Bodur
  • Mucahit Cevik
  • Juyoung Wang
    • Categories Stochastic Programming Tags , , , ,

    Multistage stochastic programming provides a modeling framework for sequential decision-making problems that involve uncertainty. One typically overlooked aspect of this methodology is how uncertainty is incorporated into modeling. Traditionally, statistical forecasting techniques with simple forms, e.g., (first-order) autoregressive time-series models, are used to extract scenarios to be added to optimization models to represent the uncertain … Read more

    A Learning Based Algorithm for Drone Routing

  • Umut Ermağan
  • Barış Yıldız
  • Sibel Salman
    • Categories Applications - OR and Management Sciences Tags , , ,

    We introduce a learning based algorithm to solve the drone routing problem with recharging stops that arises in many applications such as precision agriculture, search and rescue and military surveillance. The heuristic algorithm, namely Learn and Fly (L\&F), learns from the features of high quality solutions to optimize recharging visits, starting from a given Hamiltonian … Read more

    Routing and Wavelength Assignment with Protection: A Quadratic Unconstrained Binary Optimization Approach

  • Merve Bodur
  • Hamed Pouya
  • Oylum Şeker
    • Categories 0-1 Programming, Quadratic Programming, Telecommunications

    The routing and wavelength assignment with protection is an important problem in telecommunications. Given an optical network and incoming connection requests, a commonly studied variant of the problem aims to grant maximum number of requests by assigning lightpaths at minimum network resource usage level, while ensuring the provided services remain functional in case of a … Read more

    A Two-level ADMM Algorithm for AC OPF with Convergence Guarantees

  • Xu Andy Sun
  • Kaizhao Sun
    • Categories Constrained Nonlinear Optimization, Network Optimization, Parallel Algorithms Tags , , ,

    This paper proposes a two-level distributed algorithmic framework for solving the AC optimal power flow (OPF) problem with convergence guarantees. The presence of highly nonconvex constraints in OPF poses significant challenges to distributed algorithms based on the alternating direction method of multipliers (ADMM). In particular, convergence is not provably guaranteed for nonconvex network optimization problems … Read more