l_1 regularization – Optimization Online

A Coordinate Gradient Descent Method for L_1-regularized Convex Minimization

Published: 2008/04/23, Updated: 2010/11/30

Convex and Nonsmooth Optimization compressed sensing, convex optimization, coordinate gradient descent, image deconvolution, l_1 regularization, linear least-squares, logistic regression, q-linear convergence

In applications such as signal processing and statistics, many problems involve finding sparse solutions to under-determined linear systems of equations. These problems can be formulated as a structured nonsmooth optimization problems, i.e., the problem of minimizing L_1-regularized linear least squares problems. In this paper, we propose a block coordinate gradient descent method (abbreviated as CGD) … Read more

l_1 Trend Filtering

Published: 2007/09/29, Updated: 2022/05/13

Convex and Nonsmooth Optimization, Other Topics, Statistics detrending, feature selection, hodrick-prescott filtering, l_1 regularization, piecewise linear fitting, sparse signal recovery, time series analysis, trend estimation

The problem of estimating underlying trends in time series data arises in a variety of disciplines. In this paper we propose a variation on Hodrick-Prescott (H-P) filtering, a widely used method for trend estimation. The proposed l_1 trend filtering method substitutes a sum of absolute values (i.e., l_1-norm) for the sum of squares used in … Read more