Applications – Science and Engineering

A New Perspective on Boosting in Linear Regression via Subgradient Optimization and Relatives

  • Robert M. Freund
  • Rahul Mazumder
  • Paul Grigas
    • Categories Data-Mining, Nonsmooth Optimization, Statistics Tags , , , ,

    In this paper we analyze boosting algorithms in linear regression from a new perspective: that of modern first-order methods in convex optimization. We show that classic boosting algorithms in linear regression, namely the incremental forward stagewise algorithm (FS-epsilon) and least squares boosting (LS-Boost-epsilon), can be viewed as subgradient descent to minimize the loss function defined … Read more

    Strong SOCP Relaxations for the Optimal Power Flow Problem

  • Santanu S. Dey
  • Burak Kocuk
  • Xu Andy Sun
    • Categories Applications - Science and Engineering, Global Optimization, Nonlinear Optimization Tags , , ,

    This paper proposes three strong second order cone programming (SOCP) relaxations for the AC optimal power flow (OPF) problem. These three relaxations are incomparable to each other and two of them are incomparable to the standard SDP relaxation of OPF. Extensive computational experiments show that these relaxations have numerous advantages over existing convex relaxations in … Read more

    A proximal gradient method for ensemble density functional theory

  • Dennis Klöckner
  • Zhaosong Lu
  • Michael Ulbrich
  • Zaiwen Wen
  • Chao Yang
    • Categories Basic Sciences Applications, Constrained Nonlinear Optimization Tags , , ,

    The ensemble density functional theory is valuable for simulations of metallic systems due to the absence of a gap in the spectrum of the Hamiltonian matrices. Although the widely used self-consistent field iteration method can be extended to solve the minimization of the total energy functional with respect to orthogonality constraints, there is no theoretical … Read more

    An MILP-MINLP decomposition method for the global optimization of a source based model of the multiperiod blending problem

  • Myun-Seok Cheon
  • Ignacio E. Grossmann
  • Irene Lotero
  • Dimitri J. Papageorgiou
  • Francisco Trespalacios
    • Categories Chemical Engineering, Scheduling

    The multiperiod blending problem involves binary variables and bilinear terms, yielding a nonconvex MINLP. In this work we present two major contributions for the global solution of the problem. The rst one is an alternative formulation of the problem. This formulation makes use of redundant constraints that improve the MILP relaxation of the MINLP. The … Read more

    Exactly solving packing problems with fragmentation

  • Marco Casazza
  • Alberto Ceselli
    • Categories Applications - Science and Engineering, Combinatorial Optimization, Integer Programming Tags , , ,

    In packing problems with fragmentation a set of items of known weight is given, together with a set of bins of limited capacity; the task is to find an assignment of items to bins such that the sum of items assigned to the same bin does not exceed its capacity. As a distinctive feature, items … Read more

    Sparse optimization for inverse problems in atmospheric modelling

  • Lukáš Adam
  • Martin Branda
    • Categories 0-1 Programming, Civil and Environmental Engineering Tags , , , , ,

    We consider inverse problems in atmospheric modelling. Instead of using the ordinary least squares, we add a weighting matrix based on the topology of measurement points and show the connection with Bayesian modelling. Since the source–receptor sensitivity matrix is usually ill-conditioned, the problem is often regularized, either by perturbing the objective function or by modifying … Read more

    An extension of the projected gradient method to a Banach space setting with application in structural topology optimization

  • Luise Blank
  • Christoph Rupprecht
    • Categories Constrained Nonlinear Optimization, Control Applications, Systems governed by Differential Equations Optimization Tags , , , ,

    For the minimization of a nonlinear cost functional under convex constraints the relaxed projected gradient process is a well known method. The analysis is classically performed in a Hilbert space. We generalize this method to functionals which are differentiable in a Banach space. The search direction is calculated by a quadratic approximation of the cost … Read more

    New Improved Penalty Methods for Sparse Reconstruction Based on Difference of Two Norms

  • Yingnan Wang
    • Categories Applications - Science and Engineering, Approximation Algorithms, Nonlinear Systems and Least-Squares Tags , , , , , , , ,

    In this paper, we further establish two types of DC (Difference of Convex functions) programming for $l_0$ sparse reconstruction. Our DC objective functions are specified to the difference of two norms. One is the difference of $l_1$ and $l_{\sigma_q}$ norms (DC $l_1$-$l_{\sigma_q}$ for short) where $l_{\sigma_q}$ is the $l_1$ norm of the $q$-term ($q\geq1$) best … Read more

    Optimization of multiple receivers solar power tower systems

  • Emilio Carrizosa
  • Carmen-Ana Domínguez-Bravo
  • Enrique Fernández-Cara
  • Manuel Quero
    • Categories Applications - Science and Engineering, Multidisciplinary Design Optimization Tags , , , ,

    In this article a new procedure to optimize the design of a solar power tower system with multiple receivers is presented. The variables related to the receivers (height, aperture tilt angle, azimuth angle and aperture size) as well as the heliostat field layout are optimized seeking to minimize the levelized cost of thermal energy. This … Read more

    Machine Learning to Balance the Load in Parallel Branch-and-Bound

  • Quentin Louveaux
  • Alejandro Marcos Alvarez
  • Louis Wehenkel
    • Categories Branch and Cut Algorithms, Data-Mining

    We describe in this paper a new approach to parallelize branch-and-bound on a certain number of processors. We propose to split the optimization of the original problem into the optimization of several subproblems that can be optimized separately with the goal that the amount of work that each processor carries out is balanced between the … Read more