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An Interior Point Approach For Semidefinite Optimization Using New Proximity Functions

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  • M. REZA PEYGHAMI

    (Department of Mathematics, Faculty of Sciences, K. N. Toosi University of Technology, Tehran, Iran;
    Institute for Studies in Theoretical Physics and Mathematics (IPM), Tehran, Iran)

Abstract

Kernel functions play an important role in interior point methods (IPMs) for solving linear optimization (LO) problems to define a new search direction. In this paper, we consider primal-dual algorithms for solving Semidefinite Optimization (SDO) problems based on a new class of kernel functions defined on the positive definite cone$\mathcal{S}_{++}^{n\times n}$. Using some appealing and mild conditions of the new class, we prove with simple analysis that the new class-based large-update primal-dual IPMs enjoy an$O(\sqrt{n}\, {\rm log}\, n\, {\rm log}\, \frac{n}{\varepsilon})$iteration bound to solve SDO problems with special choice of the parameters of the new class.

Suggested Citation

  • M. Reza Peyghami, 2009. "An Interior Point Approach For Semidefinite Optimization Using New Proximity Functions," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 26(03), pages 365-382.
    • Handle: RePEc:wsi:apjorx:v:26:y:2009:i:03:n:s0217595909002250
    DOI: 10.1142/S0217595909002250
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    Cited by:

    1. Manuel V. C. Vieira, 2012. "The Accuracy of Interior-Point Methods Based on Kernel Functions," Journal of Optimization Theory and Applications, Springer, vol. 155(2), pages 637-649, November.

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