First we review the basic concepts of self-regular proximity based Interior Point Method that allowed a complexity improvement of large-update, large-scale interior point methods. Some intriguing properties of a specific self-regular proximity function are discussed and we will show that the neighborhood used in our predictor-corrector algorithm contains the infinity norm neighborhood that is used in all practical implementations of IPMs. Then a new predictor-corrector algorithm is presented where the corrector step is defined by our self-regular proximity. The worst case complexity of the proposed algorithm is O(sqrt(n) log(n) L). Our predictor-corrector algorithm has a quadratic convergence rate asymptotically. Finally, some illustrative computational results are presented. The talk is based on the results presented in: - J. Peng, C. Roos and T. Terlaky: Self-Regularity: a New Paradigm for Primal-Dual Interior Point Methods, Princeton University Press, 2002. - J. Peng, T. Terlaky and Y.B. Zhao: A predictor-corrector algorithm for linear optimization based on a self-regular proximity function. Technical Report 2003, Advanced Optimization Laboratory, McMaster University, Hamilton, Ontario, CA.