first-order methods

Convex Optimization Methods for Dimension Reduction and Coefficient Estimation in Multivariate Linear Regression

  • Zhaosong Lu
  • Renato D.C. Monteiro
  • Ming Yuan
    • Categories Convex Optimization, Nonsmooth Optimization, Statistics Tags , , , , , ,

    In this paper, we study convex optimization methods for computing the trace norm regularized least squares estimate in multivariate linear regression. The so-called factor estimation and selection (FES) method, recently proposed by Yuan et al. [17], conducts parameter estimation and factor selection simultaneously and have been shown to enjoy nice properties in both large and … Read more

    Sparse Covariance Selection via Robust Maximum Likelihood Estimation

  • Onureena Banerjeee
  • Alexandre d'Aspremont
  • Laurent El Ghaoui
    • Categories Convex Optimization, Semi-definite Programming, Statistics Tags , ,

    We address a problem of covariance selection, where we seek a trade-off between a high likelihood against the number of non-zero elements in the inverse covariance matrix. We solve a maximum likelihood problem with a penalty term given by the sum of absolute values of the elements of the inverse covariance matrix, and allow for … Read more

    First- and Second-Order Methods for Semidefinite Programming

  • Renato D.C. Monteiro
    • Categories Nonlinear Optimization, Semi-definite Programming Tags , , , , , , ,

    In this paper, we survey the most recent methods that have been developed for the solution of semidefinite programs. We first concentrate on the methods that have been primarily motivated by the interior point (IP) algorithms for linear programming, putting special emphasis in the class of primal-dual path-following algorithms. We also survey methods that have … Read more