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Homogeneous Self-dual Algorithms for Stochastic Semidefinite Programming

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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.

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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.

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Authors and Affiliations

  1. Department of Statistics, Wuhan University of Technology, Wuhan, 430063, China

    S. Jin

  2. Department of Mathematics, Washington State University, Pullman, WA, 99164-3113, USA

    K. A. Ariyawansa

  3. Division of Mathematical and Natural Sciences, Arizona State University, Phoenix, AZ, 85069-7100, USA

    Y. Zhu

Authors
  1. S. Jin
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  2. K. A. Ariyawansa
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  3. Y. Zhu
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Correspondence to K. A. Ariyawansa.

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Jin, S., Ariyawansa, K.A. & Zhu, Y. Homogeneous Self-dual Algorithms for Stochastic Semidefinite Programming. J Optim Theory Appl 155, 1073–1083 (2012). https://doi.org/10.1007/s10957-012-0110-x

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  • DOI: https://doi.org/10.1007/s10957-012-0110-x

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