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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 145323, 7 pages
Research Article

Multivariate Spectral Gradient Algorithm for Nonsmooth Convex Optimization Problems

School of Science, East China University of Science and Technology, Shanghai 200237, China

Received 20 April 2015; Revised 4 July 2015; Accepted 5 July 2015

Academic Editor: Dapeng P. Du

Copyright © 2015 Yaping Hu. 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 propose an extended multivariate spectral gradient algorithm to solve the nonsmooth convex optimization problem. First, by using Moreau-Yosida regularization, we convert the original objective function to a continuously differentiable function; then we use approximate function and gradient values of the Moreau-Yosida regularization to substitute the corresponding exact values in the algorithm. The global convergence is proved under suitable assumptions. Numerical experiments are presented to show the effectiveness of this algorithm.