International Journal of Applied Mathematics and Machine Learning[1] N. K. Karmarkar, A new polynomial-time algorithm for linear
programming, Proceedings of the 16th Annual ACM Symposium on Theory of
Computing 4 (1984), 373-395.
[2] C. Roos, T. Terlaky and J. Ph. Vial, Theory and Algorithms for
Linear Optimization, An Interior-Point Approach, John Wiley & Sons,
Chichester, UK, 1997.
[3] S. J. Wright, Primal-Dual Interior-Point Methods, SIAM,
Philadelphia, 1997.
[4] Y. Ye, Interior Point Algorithms, Theory and Analysis, John Wiley
& Sons, Chichester, UK, 1997.
[5] E. D. Andersen, J. Gondzio, Cs. Mészáros and X. Xu,
Implementation of interior point methods for large scale linear
programming, T. Terlaky, ed., Kluwer Academic Publishers, Dordrecht,
The Netherlands, (1996), 189-252.
[6] Y. Ye, A Mathematical View of Interior-Point Methods in Convex
Optimization, MPS/SIAM Ser. Optim. 3, SIAM, Philadelphia, 2001.
[7] J. Peng, C. Roos and T. Terlaky, Self-regular functions and new
search directions for linear and semidefinite optimization,
Mathematical Programming 93 (2002), 129-171.
[8] J. Peng, C. Roos and T. Terlaky, Self-Regularity: A New Paradigm
for Primal-Dual Interior-Point Algorithms, Princeton University Press,
Princeton, NJ, 2002.
[9] Y. Q. Bai, M. El Ghami and C. Roos, A new efficient large-update
primal-dual interior-point method based on a finite barrier, SIAM
Journal on Optimization 13(3) (2003), 766-782.
[10] Y. Q. Bai, M. El Ghami and C. Roos, A comparative study of kernel
functions for primal-dual interior-point algorithms in linear
optimization, SIAM Journal on Optimization 15(1) (2004), 101-128.
[11] Y. Q. Bai and C. Roos, A Primal-Dual Interior Point Method Based
on a New Kernel Function with Linear Growth Rate, Proceedings of the
9th Australian Optimization Day, Perth, Australia, 2002.
[12] Y. Q. Bai and C. Roos, A polynomial-time algorithm for linear
optimization based on a new simple kernel function, Optimization
Methods and Software 18 (2003), 631-646.
[13] Y. Q. Bai, G. Lesaja, C. Roos, G. Q. Wang and M. El Ghami, A
class of large-update and small-update primal-dual interior-point
algorithms for linear optimization, J. Optim. Theory and Appl.,
DOI: 10.1007/s10957-008-9389-z., 2008.
[14] Y. Q. Bai, J. Guo and C. Roos, A new kernel function yielding the
best known iteration bounds for primal-dual interior-point algorithms,
Acta Mathematica Sinica, English Series 49 (2007), 259-270.
[15] Y. Q. Bai, G. Q. Wang and C. Roos, Primal-dual interior point
algorithms for second-order cone optimization based on kernel
functions, Nonlinear Analysis (2008), DOI:
10.1016/j.na.2008.07.016.
[16] M. El Ghamia, I. Ivanov, J. B. M. Melissen, C. Roos and T.
Steihaug, A polynomial-time algorithm for linear optimization based on
a new class of kernel functions, Journal of Computational and Applied
Mathematics 224(2) (2009), 500-513.
[17] L. Liu and Sh. Li, A new kind of kernel function yielding good
iteration bounds for primal-dual interior-point methods, Journal of
Computational and Applied Mathematics 235 (2011), 2944-2955.
[18] M. R. Peyghami, S. F. Hafshejani and L. Shirvani, Complexity of
interior-point methods for linear optimization based on a new
trigonometric kernel function, Journal of Computational and Applied
Mathematics 255 (2014), 74-85.
[19] G. Sonnevend, An analytic center for polyhedrons and new classes
of global algorithms for linear (smooth, convex) programming, System
Modelling and Optimization: Proceedings of the 12th IFIP-Conference,
Budapest, Hungary, 1985, Lecture Notes in Control and Inform. Sci. 84,
A. Prekopa, J. Szelezsan and B. Strazicky, eds., Springer-Verlag,
Berlin, (1986), 866-876.
[20] N. Megiddo, Pathways to the optimal set in linear programming, in
Progress in Mathematical Programming: Interior Point and Related
Methods, N. Megiddo, ed., Springer-Verlag, New York, (1989),
131-158.
[21] Y. Ye, On the finite convergence of interior-point algorithms for
linear programming, Math. Program. 57 (1992), 325-335.
[22] S. Mehrotra and Y. Ye, On finding the optimal facet of linear
programs, Math. Program. 62 (1993), 497-515.
[23] C. F. Ma and X. H. Chen, The convergence of a one-step smoothing
Newton method for 
based on a new smoothing NCP-function,
Journal of Computational and Applied Mathematics 216(1) (2008), 1-13.
