Journal of Applied Mathematics
Volume 2013 (2013), Article ID 295147, 7 pages
Research Article

Parallel Variable Distribution Algorithm for Constrained Optimization with Nonmonotone Technique

1School of Mathematical Sciences, University of the Chinese Academy of Sciences, No. 19(A), Yuquan Road, Shijingshan District, Beijing 100049, China
2College of Information Science and Engineering, Shandong University of Science and Technology, Qingdao 266510, China

Received 6 September 2012; Accepted 28 February 2013

Academic Editor: Ching-Jong Liao

Copyright © 2013 Congying Han et al. 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.


A modified parallel variable distribution (PVD) algorithm for solving large-scale constrained optimization problems is developed, which modifies quadratic subproblem at each iteration instead of the of the SQP-type PVD algorithm proposed by C. A. Sagastizábal and M. V. Solodov in 2002. The algorithm can circumvent the difficulties associated with the possible inconsistency of subproblem of the original SQP method. Moreover, we introduce a nonmonotone technique instead of the penalty function to carry out the line search procedure with more flexibly. Under appropriate conditions, the global convergence of the method is established. In the final part, parallel numerical experiments are implemented on CUDA based on GPU (Graphics Processing unit).