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Mathematical Problems in Engineering
Volume 2018, Article ID 5817931, 9 pages
Research Article

The Smoothing FR Conjugate Gradient Method for Solving a Kind of Nonsmooth Optimization Problem with -Norm

School of Mathematics and Statistics, Qingdao University, Qingdao 266071, China

Correspondence should be addressed to Shou-qiang Du; nc.ude.udq@udqs

Received 9 October 2017; Accepted 27 December 2017; Published 23 January 2018

Academic Editor: Elisa Francomano

Copyright © 2018 Miao Chen and Shou-qiang Du. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We study the method for solving a kind of nonsmooth optimization problems with -norm, which is widely used in the problem of compressed sensing, image processing, and some related optimization problems with wide application background in engineering technology. Transformated by the absolute value equations, this kind of nonsmooth optimization problem is rewritten as a general unconstrained optimization problem, and the transformed problem is solved by a smoothing FR conjugate gradient method. Finally, the numerical experiments show the effectiveness of the given smoothing FR conjugate gradient method.