Primal-Dual Algorithms for Semidefinit Optimization Problems based on generalized trigonometric barrier function
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OriginalversjonEl Ghami, M. (2017). Primal-dual algorithms for semidefinit optimization problems based on generalized trigonometric barrier function. International journal of pure and applied mathematics, 114(4), 797-818. doi: 10.12732/ijpam.v114i4.10
Recently, M. Bouafoa, et al. (Journal of optimization Theory and Applications, August, 2016), investigated a new kernel function which differs from the self-regular kernel functions. The kernel function has a trigonometric Barrier Term. In this paper we generalize the analysis presented in the above paper for Semidefinit Optimization Problems (SDO). It is shown that the interior-point methods based on this function for large-update methods, the iteration bound is improved significantly. For small-update interior point methods the iteration bound is the best currently known bound for primal-dual interior point methods. The analysis for SDO deviates significantly from the analysis for linear optimization. Several new tools and techniques are derived in this paper.