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A path following interior-point algorithm for semidefinite optimization problem based on new kernel function

Citation:

Djeffal EA, Djeffal L. A path following interior-point algorithm for semidefinite optimization problem based on new kernel function. Journal of Mathematical Modeling [Internet]. 2016;4 (1) :35-58.

Abstract:

In this paper, we deal to obtain some new complexity results for solving semidefinite optimization (SDO) problem by interior-point methods (IPMs). We define a new proximity function for the SDO by a new kernel function. Furthermore we formulate an algorithm for a primal dual interior-point method (IPM) for the SDO by using the proximity function and give its complexity analysis, and then we show that the worst-case iteration bound for our IPM is O(6(m+1)3m+42(m+1)Ψm+22(m+1)01θlognμ0ε)O(6(m+1)3m+42(m+1)Ψ0m+22(m+1)1θlog⁡nμ0ε), where m>4m>4.

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