Journal of Applied Mathematics

Parallel Variable Distribution Algorithm for Constrained Optimization with Nonmonotone Technique

Congying Han, Tingting Feng, Guoping He, and Tiande Guo

Full-text: Open access

Abstract

A modified parallel variable distribution (PVD) algorithm for solving large-scale constrained optimization problems is developed, which modifies quadratic subproblem QPl at each iteration instead of the QPl0 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 QPl0 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).

Article information

Source
J. Appl. Math., Volume 2013 (2013), Article ID 295147, 7 pages.

Dates
First available in Project Euclid: 14 March 2014

Permanent link to this document
https://projecteuclid.org/euclid.jam/1394807928

Digital Object Identifier
doi:10.1155/2013/295147

Mathematical Reviews number (MathSciNet)
MR3039741

Zentralblatt MATH identifier
1266.65099

Citation

Han, Congying; Feng, Tingting; He, Guoping; Guo, Tiande. Parallel Variable Distribution Algorithm for Constrained Optimization with Nonmonotone Technique. J. Appl. Math. 2013 (2013), Article ID 295147, 7 pages. doi:10.1155/2013/295147. https://projecteuclid.org/euclid.jam/1394807928


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References

  • C. A. Sagastizábal and M. V. Solodov, “Parallel variable distribution for constrained optimization,” Computational Optimization and Applications, vol. 22, no. 1, pp. 111–131, 2002.
  • M. C. Ferris and O. L. Mangasarian, “Parallel constraint distribution,” SIAM Journal on Optimization, vol. 1, no. 1, pp. 487–500, 1994.
  • D. P. Bertsekas and J. N. Tsitsiklis, Parallel and Distributed Computation, Prentice Hall, Englewood Cliffs, NJ, USA, 1989.
  • P. Tseng, “Dual coordinate ascent methods for non-strictly convex minimization,” Mathematical Programming, vol. 59, no. 2, pp. 231–247, 1993.
  • M. V. Solodov, “New inexact parallel variable distribution algorithms,” Computational Optimization and Applications, vol. 7, no. 2, pp. 165–182, 1997.
  • M. V. Solodov, “On the convergence of constrained parallel variable distribution algorithms,” SIAM Journal on Optimization, vol. 8, no. 1, pp. 187–196, 1998.
  • F. Zheng, C. Han, and Y. Wang, “Parallel SSLE algorithm for large scale constrained optimization,” Applied Mathematics and Computation, vol. 217, no. 12, pp. 5377–5384, 2011.
  • C. Han, Y. Wang, and G. He, “On the convergence of asynchronous parallel algorithm for large-scale linearly constrained minimization problem,” Applied Mathematics and Computation, vol. 211, no. 2, pp. 434–441, 2009.
  • M. Fukushima, “Parallel variable transformation in unconstrained optimization,” SIAM Journal on Optimization, vol. 8, no. 3, pp. 658–672, 1998.
  • J. Mo, K. Zhang, and Z. Wei, “A variant of SQP method for inequality constrained optimization and its global convergence,” Journal of Computational and Applied Mathematics, vol. 197, no. 1, pp. 270–281, 2006.
  • R. Fletcher and S. Leyffer, “Nonlinear programming without a penalty function,” Mathematical Programming, vol. 91, pp. 239–269, 2002.
  • L. Grippo, F. Lampariello, and S. Lucidi, “A nonmonotone line search technique for Newton's method,” SIAM Journal on Numerical Analysis, vol. 23, no. 4, pp. 707–716, 1986.
  • L. Grippo, F. Lampariello, and S. Lucidi, “A truncated Newton method with nonmonotone line search for unconstrained optimization,” Journal of Optimization Theory and Applications, vol. 60, no. 3, pp. 401–419, 1989.
  • G. Liu, J. Han, and D. Sun, “Global convergence of the BFGS algorithm with nonmonotone linesearch,” Optimization, vol. 34, no. 2, pp. 147–159, 1995.
  • W. Sun, J. Han, and J. Sun, “Global convergence of nonmonotone descent methods for unconstrained optimization problems,” Journal of Computational and Applied Mathematics, vol. 146, no. 1, pp. 89–98, 2002.
  • P. L. Toint, “An assessment of nonmonotone linesearch techniques for unconstrained optimization,” SIAM Journal on Scientific Computing, vol. 17, no. 3, pp. 725–739, 1996.
  • K. Su and Z. Yu, “A modified SQP method with nonmonotone technique and its global convergence,” Computers & Mathematics with Applications, vol. 57, no. 2, pp. 240–247, 2009.
  • Y.-X. Yuan and W. Sun, Optimization Theory and Methods, Springer, New York, NY, USA, 2006.
  • C. T. Lawrence and A. L. Tits, “A computationally efficient feasible sequential quadratic programming algorithm,” SIAM Journal on Optimization, vol. 11, no. 4, pp. 1092–1118, 2001.
  • I. Buck, Parallel Programming with CUDA, 2008, http://gpgpu.org/sc2008.