Mixed integer formulations for a coupled lot-scheduling and vehicle routing problem in furniture settings

  • Deisemara Ferreira
  • Pedro L. Miranda
  • Reinaldo Morabito
    • Categories Production and Logistics Tags

    We propose and analyze two mathematical programming models for a production, inventory, distribution and routing problem considering real and relevant features from the furniture industry, such as production sequence-dependent setup times, heterogeneous fleet of vehicles, routes extending over one or more periods of the production planning horizon, multiple time windows and customers’ deadlines, among others. … Read more

    Run-and-Inspect Method for Nonconvex Optimization and Global Optimality Bounds for R-Local Minimizers

  • Yifan Chen
  • Wotao Yin
  • Yuejiao Sun
    • Categories Global Optimization Theory, Unconstrained Optimization Tags , , , ,

    Many optimization algorithms converge to stationary points. When the underlying problem is nonconvex, they may get trapped at local minimizers and occasionally stagnate near saddle points. We propose the Run-and-Inspect Method, which adds an “inspect” phase to existing algorithms that helps escape from non-global stationary points. The inspection samples a set of points in a … Read more

    The Strength of Multi-row Aggregation Cuts for Sign-pattern Integer Programs

  • Santanu S. Dey
  • Andres Iroume
  • Guanyi Wang
    • Categories Cutting Plane Approaches Tags , ,

    In this paper, we study the strength of aggregation cuts for sign-pattern integer programs (IPs). Sign-pattern IPs are a generalization of packing IPs and are of the form {x \in Z^n | Ax = 0} where for a given column j, A_{ij} is either non-negative for all i or non-positive for all i. Our first … Read more

    Relaxing kink qualifications and proving convergence rates in piecewise smooth optimization

  • Andreas Griewank
  • Andrea Walther
    • Categories Nonsmooth Optimization Tags , , , , , , ,

    Abstract. In the paper [9] we derived first order (KKT) and second order (SSC) optimality conditions for functions defined by evaluation programs involving smooth elementals and absolute values. In that analysis, a key assumption on the local piecewise linearization was the Linear Independence Kink Qualification (LIKQ), a generalization of the Linear Independence Constraint Qualification (LICQ) … Read more

    Nonoverlapping Domain Decomposition for Optimal Control Problems governed by Semilinear Models for Gas Flow in Networks

  • Günter Leugering
  • Martin Schmidt
  • Mathias Sirvent
  • Alexander Martin
    • Categories Applications - Science and Engineering, Systems governed by Differential Equations Optimization Tags , , , ,

    We consider optimal control problems for gas flow in pipeline networks. The equations of motion are taken to be represented by a first-order system of hyperbolic semilinear equations derived from the fully nonlinear isothermal Euler gas equations. We formulate an optimal control problem on a network and introduce a tailored time discretization thereof. In order … Read more

    Multi-objective risk-averse two-stage stochastic programming problems

  • Cagin Ararat
  • Özlem Cavus
  • Ali Irfan Mahmutogullari
    • Categories Stochastic Programming Tags , , , , , ,

    We consider a multi-objective risk-averse two-stage stochastic programming problem with a multivariate convex risk measure. We suggest a convex vector optimization formulation with set-valued constraints and propose an extended version of Benson’s algorithm to solve this problem. Using Lagrangian duality, we develop scenario-wise decomposition methods to solve the two scalarization problems appearing in Benson’s algorithm. … Read more

    Adaptive Fista

  • Peter Ochs
  • Thomas Pock
    • Categories Convex and Nonsmooth Optimization Tags , , ,

    In this paper we propose an adaptively extrapolated proximal gradient method, which is based on the accelerated proximal gradient method (also known as FISTA), however we locally optimize the extrapolation parameter by carrying out an exact (or inexact) line search. It turns out that in some situations, the proposed algorithm is equivalent to a class … Read more

    An Accelerated Communication-Efficient Primal-Dual Optimization Framework for Structured Machine Learning

  • Frank E. Curtis
  • Martin Jaggi
  • Chenxin Ma
  • Nathan Srebro
  • Martin Takac
    • Categories Nonlinear Optimization, Parallel Algorithms

    Distributed optimization algorithms are essential for training machine learning models on very large-scale datasets. However, they often suffer from communication bottlenecks. Confronting this issue, a communication-efficient primal-dual coordinate ascent framework (CoCoA) and its improved variant CoCoA+ have been proposed, achieving a convergence rate of $\mathcal{O}(1/t)$ for solving empirical risk minimization problems with Lipschitz continuous losses. … Read more

    On the use of third-order models with fourth-order regularization for unconstrained optimization

  • Ernesto G. Birgin
  • José Mario Martínez
  • Sandra Augusta Santos
  • John L. Gardenghi
    • Categories Unconstrained Optimization Tags , , ,

    In a recent paper, it was shown that, for the smooth unconstrained optimization problem, worst-case evaluation complexity $O(\epsilon^{-(p+1)/p})$ may be obtained by means of algorithms that employ sequential approximate minimizations of p-th order Taylor models plus (p + 1)-th order regularization terms. The aforementioned result, which assumes Lipschitz continuity of the p-th partial derivatives, generalizes … Read more

    Meta-Modeling to Assess the Possible Future of Paris Agreement

  • Frédéric Babonneau
  • A Bernard
  • Alain Haurie
  • Alain Vielle
    • Categories Game Theory Tags , , , , , ,

    In the meta-modeling approach one builds a numerically tractable dynamic optimization or game model in which the parameters are identified through statistical emulation of a detailed large scale numerical simulation model. In this paper we show how this approach can be used to assess the economic impacts of possible climate policies compatible with the Paris … Read more