Applications – Science and Engineering

A Fixed-Point Continuation Method for l_1-Regularized Minimization with Applications to Compressed Sensing

  • Elaine Hale
  • Wotao Yin
  • Yin Zhang
    • Categories Applications - Science and Engineering, Convex Optimization, Nonsmooth Optimization Tags , , , ,

    We consider solving minimization problems with $\ell_1$-regularization: $$\min \|x\|_1 + \mu f(x),$$ particularly for $f(x) = \frac{1}{2}\|Ax-b\|_M^2$ where $A \in \R^{m \times n}$ with $m < n$. Our goal is to construct efficient and robust algorithms for solving large-scale problems with dense data, and our approach is based on two powerful algorithmic ideas, operator-splitting and ... Read more

    Optimization for Simulation: LAD Accelerator

  • Miguel A. Lejeune
  • François Margot
    • Categories Data-Mining, Optimization of Simulated Systems, Stochastic Approaches Tags , ,

    The goal of this paper is to address the problem of evaluating the performance of a system running under unknown values for its stochastic parameters. A new approach called LAD for Simulation, based on simulation and classification software, is presented. It uses a number of simulations with very few replications and records the mean value … Read more

    Smooth Optimization Approach for Covariance Selection

  • Zhaosong Lu
    • Categories Convex and Nonsmooth Optimization, Statistics Tags , ,

    In this paper we study a smooth optimization approach for solving a class of non-smooth {\it strongly} concave maximization problems. In particular, we apply Nesterov’s smooth optimization technique \cite{Nest83-1,Nest05-1} to their dual counterparts that are smooth convex problems. It is shown that the resulting approach has $\cO(1/{\sqrt{\epsilon}})$ iteration complexity for finding an $\epsilon$-optimal solution to … Read more

    Gradient Projection for Sparse Reconstruction: Application to Compressed Sensing and Other Inverse Problems

  • Mario A. T. Figueiredo
  • Stephen Wright
  • Robert Nowak
    • Categories Applications - Science and Engineering, Bound-constrained Optimization Tags ,

    Many problems in signal processing and statistical inference involve finding sparse solutions to under-determined, or ill-conditioned, linear systems of equations. A standard approach consists in minimizing an objective function which includes a quadratic (squared $\ell_2$) error term combined with a sparseness-inducing ($\ell_1$) regularization term.{\it Basis pursuit}, the {\it least absolute shrinkage and selection operator} (LASSO), … Read more

    Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization

  • Maryam Fazel
  • Benjamin Recht
  • Pablo A. Parrilo
    • Categories Convex and Nonsmooth Optimization, Semi-definite Programming, Statistics Tags , , ,

    The affine rank minimization problem consists of finding a matrix of minimum rank that satisfies a given system of linear equality constraints. Such problems have appeared in the literature of a diverse set of fields including system identification and control, Euclidean embedding, and collaborative filtering. Although specific instances can often be solved with specialized algorithms, … Read more

    An iterative approach for cone complementarity problems for nonsmooth multibody dynamics

  • Mihai Anitescu
  • Alessandro Tasora
    • Categories Complementarity and Variational Inequalities, Convex Optimization, Mechanical Engineering

    Aiming at a fast and robust simulation of large multibody systems with contacts and friction, this work presents a novel method for solving large cone complementarity problems by means of a fixed-point iteration. The method is an extension of the Gauss-Seidel and Gauss-Jacobi method with overrelaxation for symmetric convex linear complementarity problems. The method is … Read more

    Graph Modeling for Quadratic Assignment Problem Associated with the Hypercube

  • Hans D Mittelmann
  • Jiming Peng
  • Xiaolin Wu
    • Categories Applications - Science and Engineering, Graphs and Matroids, Telecommunications Tags

    In the paper we consider the quadratic ssignment problem arising from channel coding in communications where one coefficient matrix is the adjacency matrix of a hypercube in a finite dimensional space. By using the geometric structure of the hypercube, we first show that there exist at least $n$ different optimal solutions to the underlying QAPs. … Read more

    A Coordinate Gradient Descent Method for Linearly Constrained Smooth Optimization and Support Vector Machines Training

  • Paul Tseng
  • Sangwoon Yun
    • Categories Constrained Nonlinear Optimization, Data-Mining Tags , , , , , , , ,

    Support vector machines (SVMs) training may be posed as a large quadratic program (QP) with bound constraints and a single linear equality constraint. We propose a (block) coordinate gradient descent method for solving this problem and, more generally, linearly constrained smooth optimization. Our method is closely related to decomposition methods currently popular for SVM training. … Read more

    Exploiting group symmetry in truss topology optimization

  • Yanqin Bai
  • Etienne de Klerk
  • Renata Sotirov
  • Dmitrii V. Pasechnik
    • Categories Applications - Science and Engineering, Semi-definite Programming Tags , ,

    We consider semidefinite programming (SDP) formulations of certain truss topology optimization problems, where a lower bound is imposed on the fundamental frequency of vibration of the truss structure. These SDP formulations were introduced in: [M. Ohsaki, K. Fujisawa, N. Katoh and Y. Kanno, Semi-definite programming for topology optimization of trusses under multiple eigenvalue constraints, Comp. … Read more

    Modeling and Simulation of Metabolic Networks for Estimation of Biomass Accumulation Parameters

  • Lorenz T. Biegler
  • Bulent Karasozen
  • Metin Turkay
  • Ugur Kaplan
    • Categories Biomedical Applications, Systems governed by Differential Equations Optimization Tags , ,

    Metabolic networks are defined as the collection of biochemical reactions within a cell that define the functions of that cell. Due to the growing need to understand the functions of biological organisms for industrial and medical purposes, modeling and simulation of metabolic networks has attracted a lot of attention recently. Traditionally, metabolic networks are modeled … Read more