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Journal of Applied Mathematics
Volume 2010 (2010), Article ID 307209, 19 pages
http://dx.doi.org/10.1155/2010/307209
Research Article

Constraint Consensus Methods for Finding Interior Feasible Points in Second-Order Cones

1Department of Mathematics, Illinois State University, Normal, IL 61790-4520, USA
2Department of Mathematics, Saint Michael's College, Colchester, VT 05439, USA
3Department of Mathematics and Statistics, Northern Arizona University, Flagstaff, AZ 86011-5717, USA

Received 29 August 2010; Revised 17 November 2010; Accepted 17 December 2010

Academic Editor: Tak-Wah Lam

Copyright © 2010 Anna Weigandt 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.

Linked References

  1. M. S. Lobo, L. Vandenberghe, S. Boyd, and H. Lebret, “Applications of second-order cone programming,” Linear Algebra and Its Applications, vol. 284, no. 1–3, pp. 193–228, 1998. View at Publisher · View at Google Scholar
  2. F. Alizadeh and D. Goldfarb, “Second-order cone programming,” Mathematical Programming, vol. 95, no. 1, pp. 3–51, 2003. View at Publisher · View at Google Scholar
  3. J. W. Chinneck, “The constraint consensus method for finding approximately feasible points in nonlinear programs,” Informs Journal on Computing, vol. 16, no. 3, pp. 255–265, 2004. View at Google Scholar
  4. Y. Nesterov and A. Nemirovsky, “Interior-Point polynomial methods in convex programming,” in Studies in Applied Mathematics, vol. 13, SIAM, Philadelphia, Pa, USA, 1994. View at Google Scholar
  5. R. J. Caron, T. Traynor, and S. Jibrin, “Feasibility and constraint analysis of sets of linear matrix inequalities,” Informs Journal on Computing, vol. 22, no. 1, pp. 144–153, 2010. View at Google Scholar
  6. J. W. Chinneck, Private communication with S. Jibrin, 2010.
  7. D. den Hertog, Interior Point Approach to Linear, Quadratic and Convex Programming, vol. 277 of Mathematics and Its Applications, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1994.
  8. R. J. Vanderbei, Linear Programming: Foundations and Extensions, Kluwer Academic Publishers, Boston, Mass, USA, Second edition, 2001.
  9. W. Ibrahim and J. W. Chinneck, “Improving solver success in reaching feasibility for sets of nonlinear constraints,” Computers & Operations Research, vol. 35, no. 5, pp. 1394–1411, 2008. View at Publisher · View at Google Scholar
  10. Y. Censor and S. A. Zenios, Parallel Optimization: Theory, Algorithms, and Applications, Numerical Mathematics and Scientific Computation, Oxford University Press, New York, NY, USA, 1997.
  11. D. Butnariu, Y. Censor, and S. Reich, Inherently Parallel Algorithms in Feasibility and Optimization and Their Applications, vol. 8 of Studies in Computational Mathematics, North-Holland Publishing, Amsterdam, The Netherlands, 2001.