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

    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

    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

    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

    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

    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

    Uniqueness and Multiplicity of Market Equilibria on DC Power Flow Networks

  • Vanessa Krebs
  • Lars Schewe
  • Martin Schmidt
    • Categories Applications - OR and Management Sciences, Convex Optimization, Network Optimization Tags , , , , ,

    We consider uniqueness and multiplicity of market equilibria in a short-run setup where traded quantities of electricity are transported through a capacitated network in which power flows have to satisfy the classical lossless DC approximation. The firms face fluctuating demand and decide on their production, which is constrained by given capacities. Today, uniqueness of such … Read more

    NeatWork, a tool for the design of gravity-driven water distribution systems for poor rural communities

  • Frédéric Babonneau
  • Jean-Philippe Vial
  • G Corcos
  • L Drouet
    • Categories Applications - OR and Management Sciences, Applications - Science and Engineering Tags , , ,

    NeatWork is an advanced optimization and simulation tool for the design of purely gravity-driven water distribution systems aiming at delivering clean water to poor rural communities. The exclusion of any adjustable devices, such as pumps and valves, for controlling pressures and flows is motivated by two main reasons: firstly, the system should be as simple … Read more

    Energy Technology Environment Model with Smart Grid and Robust Nodal Electricity Prices

  • Frédéric Babonneau
  • Alain Haurie
    • Categories Applications - OR and Management Sciences, Applications - Science and Engineering

    This paper deals with the modeling of power flow in a transmission grid within the multi-sectoral multi-energy long-term regional energy model ETEM-SG. This extension of the model allows a better representation of demand response for flexible loads triggered by nodal marginal cost pricing. To keep the global model in the realm of linear program- ming … 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