Month: October 2017

A Dense initialization for limited-memory quasi-Newton methods

  • Johannes Brust
  • Oleg Burdakov
  • Jennifer B. Erway
  • Roummel F. Marcia
    • Categories Nonlinear Optimization, Unconstrained Optimization Tags , , , ,

    We consider a family of dense initializations for limited-memory quasi-Newton methods. The proposed initialization exploits an eigendecomposition-based separation of the full space into two complementary subspaces, assigning a different initialization parameter to each subspace. This family of dense initializations is proposed in the context of a limited-memory Broyden- Fletcher-Goldfarb-Shanno (L-BFGS) trust-region method that makes use … Read more

    The forwarder planning problem in a two-echelon network

  • Massimo Di Francesco
  • Manlio Gaudioso
  • Enrico Gorgone
  • Paola Zuddas
    • Categories Approximation Algorithms, Transportation Tags , ,

    This paper is motivated by the case of a forwarder in dealing with inland transportation planning from a seaport, where inbound containers from the sea are filled with pallets, which have different destinations in the landside. Although this forwarder does not have or control any vehicle, he is required to plan the assignment of containers … Read more

    Minimizer extraction in polynomial optimization is robust

  • Igor Klep
  • Janez Povh
  • Jurij Volčič
    • Categories Semi-definite Programming Tags , , , , , , , ,

    In this article we present a robustness analysis of the extraction of optimizers in polynomial optimization. Optimizers can be extracted by solving moment problems using flatness and the Gelfand-Naimark-Segal (GNS) construction. Here a modification of the GNS construction is presented that applies even to non-flat data, and then its sensitivity under perturbations is studied. The … Read more

    Enriching Solutions to Combinatorial Problems via Solution Engineering

  • Petit Thierry
  • Andrew C. Trapp
    • Categories Combinatorial Optimization Tags , , , ,

    Existing approaches to identify multiple solutions to combinatorial problems in practice are at best limited in their ability to simultaneously incorporate both diversity among generated solutions, as well as problem-specific desires that are apriori unknown, or at least difficult to articulate, for the end-user. We propose a general framework that can generate a set of … Read more

    A multi-period production and distribution optimization model for radiopharmaceuticals

  • Ioannis G. Akrotirianakis
  • Amit Chakraborty
    • Categories (Mixed) Integer Nonlinear Programming, Biomedical Applications, Production and Logistics Tags , , ,

    This paper addresses the manufacturing and distribution of short-lived radio-pharmaceuticals which are mainly used in diagnostic imaging studies. We develop a mixed integer nonlinear optimization model that is flexible enough to capture the complex underlying nuclear physics of the production process of fludeoxyglucose (FDG), which is widely used in oncology and cardiology, as well as … Read more

    Primal-Dual Optimization Algorithms over Riemannian Manifolds: an Iteration Complexity Analysis

  • Shiqian Ma
  • Junyu Zhang
  • Shuzhong Zhang
    • Categories Constrained Nonlinear Optimization Tags , , , ,

    In this paper we study nonconvex and nonsmooth multi-block optimization over Riemannian manifolds with coupled linear constraints. Such optimization problems naturally arise from machine learning, statistical learning, compressive sensing, image processing, and tensor PCA, among others. We develop an ADMM-like primal-dual approach based on decoupled solvable subroutines such as linearized proximal mappings. First, we introduce … Read more

    On the equivalence of the primal-dual hybrid gradient method and Douglas-Rachford splitting

  • Daniel O'Connor
  • Lieven Vandenberghe
    • Categories Convex and Nonsmooth Optimization Tags , , ,

    The primal-dual hybrid gradient (PDHG) algorithm proposed by Esser, Zhang, and Chan, and by Pock, Cremers, Bischof, and Chambolle is known to include as a special case the Douglas-Rachford splitting algorithm for minimizing the sum of two convex functions. We show that, conversely, the PDHG algorithm can be viewed as a special case of the … Read more

    Tightness of a new and enhanced semidefinite relaxation for MIMO detection

  • Ya-Feng Liu
  • Cheng Lu
  • Wei-Qiang Zhang
  • Shuzhong Zhang
    • Categories Global Optimization Applications, Semi-definite Programming, Telecommunications Tags , , ,

    In this paper, we consider a fundamental problem in modern digital communications known as multi-input multi-output (MIMO) detection, which can be formulated as a complex quadratic programming problem subject to unit-modulus and discrete argument constraints. Various semidefinite relaxation (SDR) based algorithms have been proposed to solve the problem in the literature. In this paper, we … Read more

    Balancing Communication and Computation in Distributed Optimization

  • Albert S. Berahas
  • Raghu Bollapragada
  • Nitish Shirish Keskar
  • Ermin Wei
    • Categories Convex Optimization, Distributed Control, Network Optimization Tags , , , ,

    Methods for distributed optimization have received significant attention in recent years owing to their wide applicability in various domains including machine learning, robotics and sensor networks. A distributed optimization method typically consists of two key components: communication and computation. More specifically, at every iteration (or every several iterations) of a distributed algorithm, each node in … Read more

    Globally Solving the Trust Region Subproblem Using Simple First-Order Methods

  • Amir Beck
  • Yakov Vaisbourd
    • Categories Constrained Nonlinear Optimization Tags , , , ,

    We consider the trust region subproblem which is given by a minimization of a quadratic, not necessarily convex, function over the Euclidean ball. Based on the well-known second-order necessary and sufficient optimality conditions for this problem, we present two sufficient optimality conditions defined solely in terms of the primal variables. Each of these conditions corresponds … Read more