Applications – Science and Engineering

An inexact interior point method for L1-regularized sparse covariance selection

  • Lu Li
  • Kim-Chuan Toh
    • Categories Convex Optimization, Semi-definite Programming, Statistics Tags , , , ,

    Sparse covariance selection problems can be formulated as log-determinant (log-det) semidefinite programming (SDP) problems with large numbers of linear constraints. Standard primal-dual interior-point methods that are based on solving the Schur complement equation would encounter severe computational bottlenecks if they are applied to solve these SDPs. In this paper, we consider a customized inexact primal-dual … Read more

    On Computation of Performance Bounds of Optimal Index Assignment

  • Hans D Mittelmann
  • Xiaolin Wu
  • J. Wang
  • X. Wang
    • Categories Applications - Science and Engineering, Semi-definite Programming Tags , , , , ,

    Channel-optimized index assignment of source codewords is arguably the simplest way of improving transmission error resilience, while keeping the source and/or channel codes intact. But optimal design of index assignment is an in- stance of quadratic assignment problem (QAP), one of the hardest optimization problems in the NP-complete class. In this paper we make a … Read more

    Optimal location of family homes for dual career couples

  • Andrea Abele
  • Martin Gugat
  • Kathrin Klamroth
    • Categories Applications - OR and Management Sciences, Facility Planning and Design, Multi-Criteria Optimization Tags , , , ,

    The number of dual-career couples with children is growing fast. These couples face various challenging problems of organizing their lifes, in particular connected with childcare and time-management. As a typical example we study one of the difficult decision problems of a dual career couple from the point of view of operations research with a particular … Read more

    Sparse optimization with least-squares constraints

  • Michael P. Friedlander
  • Ewout van den Berg
    • Categories Applications - Science and Engineering, Nonsmooth Optimization Tags , , , , , , ,

    The use of convex optimization for the recovery of sparse signals from incomplete or compressed data is now common practice. Motivated by the success of basis pursuit in recovering sparse vectors, new formulations have been proposed that take advantage of different types of sparsity. In this paper we propose an efficient algorithm for solving a … Read more

    On Low Rank Matrix Approximations with Applications to Synthesis Problem in Compressed Sensing

  • Anatoli Juditsky
  • Fatma Kılınç-Karzan
  • Arkadi Nemirovski
    • Categories Basic Sciences Applications, Stochastic Programming Tags ,

    We consider the synthesis problem of Compressed Sensing: given $s$ and an $M\times n$ matrix $A$, extract from $A$ an $m\times n$ submatrix $A_m$, with $m$ as small as possible, which is $s$-good, that is, every signal $x$ with at most $s$ nonzero entries can be recovered from observation $A_m x$ by $\ell_1$ minimization: $x … Read more

    A Pure L1-norm Principal Component Analysis

  • E.L. Boone
  • J. Paul Brooks
  • JH Dulá
    • Categories Data-Mining, Linear Programming Tags , ,

    The L1 norm has been applied in numerous variations of principal component analysis (PCA). L1-norm PCA is an attractive alternative to traditional L2-based PCA because it can impart robustness in the presence of outliers and is indicated for models where standard Gaussian assumptions about the noise may not apply. Of all the previously-proposed PCA schemes … Read more

    Recovering low-rank and sparse components of matrices from incomplete and noisy observations

  • Tao Min
  • Xiao-Ming Yuan
    • Categories Convex Optimization, Statistics Tags , , , , ,

    Many applications arising in a variety of fields can be well illustrated by the task of recovering the low-rank and sparse components of a given matrix. Recently, it is discovered that this NP-hard task can be well accomplished, both theoretically and numerically, via heuristically solving a convex relaxation problem where the widely-acknowledged nuclear norm and … Read more

    On the Effectiveness of Projection Methods for Convex Feasibility

  • Yair Censor
  • Patrick L. Combettes
  • Wei Chen
  • Ran Davidi
  • Gabor T. Herman
    • Categories Applications - Science and Engineering, Biomedical Applications, Linear, Cone and Semidefinite Programming

    The effectiveness of projection methods for solving systems of linear inequalities is investigated. It is shown that they have a computational advantage over some alternatives and that this makes them successful in real-world applications. This is supported by experimental evidence provided in this paper on problems of various sizes (up to tens of thousands of … Read more

    Metal Artefact Reduction by Least-Squares Penalized-Likelihood Reconstruction with a Fast Polychromatic Projection Model

  • Jean-Pierre Dussault
  • Yves Goussard
  • Benoit Hamelin
    • Categories Biomedical Applications, Bound-constrained Optimization Tags , , , , ,

    We consider penalized-likelihood reconstruction for X-ray computed tomography of objects that contain small metal structures. To reduce the beam hardening artefacts induced by these structures, we derive the reconstruction algorithm from a projection model that takes into account the photon emission spectrum and nonlinear variation of attenuation to photon energy. This algorithm requires excessively long … Read more

    Multidisciplinary Free Material Optimization

  • J Haslinger
  • Michal Kočvara
  • Günter Leugering
  • Michael Stingl
    • Categories Mechanical Engineering, Multidisciplinary Design Optimization, Semi-definite Programming Tags , , , ,

    We present a mathematical framework for the so-called multidisciplinary free material optimization (MDFMO) problems, a branch of structural optimization in which the full material tensor is considered as a design variable. We extend the original problem statement by a class of generic constraints depending either on the design or on the state variables. Among the … Read more