Journal of Optimization Theory and Applications

, Volume 155, Issue 3, pp 1073–1083 | Cite as

Homogeneous Self-dual Algorithms for Stochastic Semidefinite Programming

Article
First Online:
Received:
Accepted:

Abstract

Ariyawansa and Zhu have proposed a new class of optimization problems termed stochastic semidefinite programs to handle data uncertainty in applications leading to (deterministic) semidefinite programs. For stochastic semidefinite programs with finite event space, they have also derived a class of volumetric barrier decomposition algorithms, and proved polynomial complexity of certain members of the class. In this paper, we consider homogeneous self-dual algorithms for stochastic semidefinite programs with finite event space. We show how the structure in such problems may be exploited so that the algorithms developed in this paper have complexity similar to those of the decomposition algorithms mentioned above.

Keywords

Semidefinite programming Homogeneous self-dual algorithms Computational complexity Stochastic semidefinite programming 
This is a preview of subscription content, log in to check access.

Notes

Acknowledgements

The work of S.J. was performed while he was visiting Washington State University. Research supported in part by the Chinese National Foundation under Grants No. 51139005 and 51179147. K.A.A. research supported in part by the US Army Research Office under Grant DAAD 19-00-1-0465 and by Award W11NF-08-1-0530. Y.Z. research supported in part by ASU West MGIA Grant 2007.

References

  1. 1.
    Kall, P., Wallace, S.: Stochastic Programming. Wiley, New York (1994) MATHGoogle Scholar
  2. 2.
    Todd, M.J.: Semidefinite optimization. Acta Numer. 10, 515–560 (2001) MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    Ariyawansa, K.A., Zhu, Y.: Stochastic semidefinite programming: a new paradigm for stochastic optimization. 4OR 4(3), 239–253 (2006). An earlier version of this paper appeared as Technical Report 2004-10 of the Department of Mathematics, Washington State University, Pullman, WA 99164-3113, in October 2004 MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    Ariyawansa, K.A., Zhu, Y.: A class of polynomial volumetric barrier decomposition algorithms for stochastic semidefinite programming. Math. Comput. 80, 1639–1661 (2011) MathSciNetMATHCrossRefGoogle Scholar
  5. 5.
    Todd, M.J., Toh, K.C., Tütüncü, R.H.: On the Nesterov-Todd direction in semidefinite programming. SIAM J. Optim. 8, 769–796 (1998) MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    Potra, F., Sheng, R.: On homogeneous interior-point algorithms for semidefinite programming. Optim. Methods Softw. 9, 161–184 (1998) MathSciNetMATHCrossRefGoogle Scholar
  7. 7.
    Toh, K.C., Todd, M.J., Tütüncü, R.H.: SDPT3—a MATLAB software package for semidefinite programming. Optim. Methods Softw. 11/12, 545–581 (1999) CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of StatisticsWuhan University of TechnologyWuhanChina
  2. 2.Department of MathematicsWashington State UniversityPullmanUSA
  3. 3.Division of Mathematical and Natural SciencesArizona State UniversityPhoenixUSA

Personalised recommendations