Abstract
Interior-point methods (IPMs) for semidefinite optimization (SDO) have been studied intensively, due to their polynomial complexity and practical efficiency. Recently, J. Peng et al. introduced so-called self-regular kernel (and barrier) functions and designed primal-dual interior-point algorithms based on self-regular proximities for linear optimization (LO) problems. They also extended the approach for LO to SDO. In this paper we present a primal-dual interior-point algorithm for SDO problems based on a simple kernel function which was first presented at the Proceedings of Industrial Symposium and Optimization Day, Australia, November 2002; the function is not self-regular. We derive the complexity analysis for algorithms based on this kernel function, both with large- and small-updates. The complexity bounds are and , respectively, which are as good as those in the linear case.
Keywords semidefinite optimization - interior-point methods - primal-dual methods - large- and small-update methods - polynomial complexity
Mathematics Subject Classifications (2000) 90C22, 90C31.
Original language | Undefined/Unknown |
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Pages (from-to) | 409-433 |
Number of pages | 25 |
Journal | Journal of Mathematical Modelling and Algorithms |
Volume | 4 |
Issue number | 4 |
DOIs | |
Publication status | Published - 2005 |
Keywords
- academic journal papers
- Vakpubl., Overig wet. > 3 pag