A second-order corrector wide neighborhood infeasible interior-point method for linear optimization based on a specific kernel function

1] W. Ai, Neighborhood-following algorithms for linear programming, Science in China Series A: Mathematics 47 (2004), no. 6, 812–820.

[2] W. Ai and S. Zhang, An O(√nl) iteration primal-dual path-following method, based on wide neighborhoods and large updates, for monotone LCP, SIAM J. Optim. 16 (2005), no. 2, 400–417.

[3] 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 J. Optim. 15 (2004), no. 1, 101–128.

[4] Zs. Darvay, A new predictor-corrector algorithm for linear programming, Alkalmazott Matematikai Lapok (in Hungarian) 22 (2005), 135–161.

[5] Z. Feng, A new iteration large-update primal-dual interior-point method for second-order cone programming, Numer. Func. Anal. Optim. 33 (2012), no. 4, 397–414.

[6] Z. Feng and L. Fang, A new O(√nl) -iteration predictor-corrector algorithm with wide neighborhood for semidefinite programming, J. Comput. Appl. Math. 256 (2014), 65–76.

[7] N.K. Karmarkar, A new polynomial-time algorithm for linear programming, Combinatorica 4 (1984), no. 4, 373–395.

[8] B. Kheirfam, A predictor-corrector interior-point algorithm for P∗(κ)-horizontal linear complementarity problem, Numer. Algorithms 66 (2014), no. 2, 349–361.

[9] B. Kheirfam, A corrector–predictor path-following method for convex quadratic symmetric cone optimization, J. Optim. Theory Appl. 164 (2015), no. 1, 246–260.

[10] B. Kheirfam, A corrector–predictor path-following method for second-order cone optimization, Int. J. Comput. Math. 93 (2016), no. 12, 2064–2078.

[11] B. Kheirfam, A predictor-corrector infeasible-interior-point algorithm for semidefinite optimization in a wide neighborhood, Fundam. Inform. 152 (2017), no. 1, 33–50.

[12] B. Kheirfam and M. Chitsaz, A new second-order corrector interior-point algorithm for P∗(κ)-LCP, Filomat 31 (2017), no. 20, 6379–6391.

[13] B. Kheirfam and M. Haghighi, A wide neighborhood interior-point algorithm for linear optimization based on a specific kernel function, Period. Math. Hung. 79 (2019), no. 1, 94–105.

[14] B. Kheirfam and M. Mohamadi-Sangachin, A wide neighborhood second-order predictor-corrector interior-point algorithm for semidefinite optimization with modified corrector directions, Fundam. Inform. 153 (2017), no. 4, 327–346.

[15] Y. Li and T. Terlaky, A new class of large neighborhood path-following interior point algorithms for semidefinite optimization with O(√n log(tr(x⁰s⁰)/ε)) iteration complexity, SIAM J. Optim. 20 (2010), no. 6, 2853–2875.

[16] C. Liu and H. Liu, A new second-order corrector interior-point algorithm for semidefinite programming, Math. Meth. Oper. Res. 75 (2012), no. 2, 165–183.

17] H. Liu, X. Yang, and C. Liu, A new wide neighborhood primal–dual infeasibleinterior-point method for symmetric cone programming, J. Optim. Theory Appl. 158 (2013), no. 3, 796–815.

[18] N. Megiddo, Pathways to the optimal set in linear programming, Progress in Mathematical Programming, Springer-Verlag, New York, 1989, pp. 131–158.

[19] S. Mehrotra, On the implementation of a primal-dual interior point method, SIAM J. Optim. 2 (1992), no. 4, 575–601.

[20] S. Mizuno, M.J. Todd, and Y. Ye, On adaptive-step primal-dual interior-point algorithms for linear programming, Math. Oper. Res. 18 (1993), no. 4, 964–981.

[21] J. Peng, C. Roos, and T. Terlaky, Self-regular functions and new search directions for linear and semidefinite optimization, Math. Program. 93 (2002), no. 1, 129–171.

[22] F.A. Potra, Interior point methods for sufficient horizontal LCP in a wide neighborhood of the central path with best known iteration complexity, SIAM J. Optim. 24 (2014), no. 1, 1–28.

[23] C. Roos, T. Terlaky, and J.-P. Vial, Theory and algorithms for linear optimization: an interior point approach, John Wiley & Sons, Chichester, UK, 1997.

[24] G. Sonnevend, An “analytic center” for polyhedrons and new classes of global algorithms for linear (smooth, convex) optimization, In A. Pr´ekopa and J. Szelezs´an and B. Strazicky editor, System Modelling and Optimization: Proceedings of the 12th IFIP-Conference held in Budapest, Hungary, September 1985, Lecture Notes in Control and Information Sciences, 84, Springer Verlag, Berlin, West-Germany, 1986, pp. 866–876.

[25] G.-Q. Wang and Y.-Q. Bai, A new full nesterov–todd step primal–dual pathfollowing interior-point algorithm for symmetric optimization, J. Optim. Theory Appl. 154 (2012), no. 3, 966–985.

[26] G.Q. Wang, Y.Q. Bai, X.Y. Gao, and D.Z. Wang, Improved complexity analysis of full Nesterov–Todd step interior-point methods for semidefinite optimization, J. Optim. Theory Appl. 165 (2015), no. 1, 242–262.

[27] G.Q. Wang, X.J. Fan, D.T. Zhu, and D.Z. Wang, New complexity analysis of a full-newton step feasible interior-point algorithm for P∗(κ)-LCP, Optim. Lett. 9 (2015), no. 6, 1105–1119.

[28] S.J. Wright, Primal-Dual Interior-Point Methods, SIAM, 1997.

[29] Y. Ye, Interior Point Algorithms: Theory and Analysis, vol. 44, John Wiley & Sons Inc., New York, 1997.

[30] Y. Zhang and D. Zhang, On polynomiality of the mehrotra-type predictor–corrector interior-point algorithms, Math. Program. 68 (1995), no. 1, 303–318.