AN INTERIOR POINT APPROACH FOR SEMIDEFINITE OPTIMIZATION USING NEW PROXIMITY FUNCTIONS

M. Reza Peyghami ()
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M. Reza Peyghami: Department of Mathematics, Faculty of Sciences, K. N. Toosi University of Technology, Tehran, Iran;

Asia-Pacific Journal of Operational Research (APJOR), 2009, vol. 26, issue 03, 365-382

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.

Keywords: Semidefinite optimization; primal-dual interior-point method; large-update method; polynomial complexity; 90C22; 90C31 (search for similar items in EconPapers)
Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:wsi:apjorx:v:26:y:2009:i:03:n:s0217595909002250

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DOI: 10.1142/S0217595909002250

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