New predictor-corrector interior-point algorithm for symmetric cone horizontal linear complementarity problems

Achache, M.: A new primal-dual path-following method for convex quadratic programming, Comput. Appl.
Math. 25, 97-110 (2006)

Asadi, S., Mahdavi-Amiri, N., Darvay, Zs., Rigó, P.R.: Full-NT step feasible interior-point algorithm for symmetric
cone horizontal linear complementarity problem based on a positive-asymptotic barrier function, Optim.
Methods Sofw., DOI: 10.1080/10556788.2020.1734803 (2020)

Asadi, S., Mansouri, H., Darvay, Zs.: An infeasible full-NT step IPM for P_*(κ) horizontal linear complementarity
problem over Cartesian product of symmetric cones, Optimization 66, 225-250 (2017)

Asadi, S., Mansouri, H., Darvay, Zs., Zangiabadi, M.: On the P_*(κ) horizontal linear complementarity problems
over Cartesian product of symmetric cones, Optim. Methods Softw. 31, 233-257 (2016)

Asadi, S., Zangiabadi, M., Mansouri, H.: A predictor-corrector interior-point algorithm for P_*(κ)-HLCPs over
Cartesian product of symmetric cones, Numer. Func. Anal. Optim. 38, 20-38 (2017)

Asadi, S., Mansouri, H., Lesaja, G., Zangiabadi, M.: A long-step interior-point algorithm for symmetric cone
Cartesian P_*(κ)-HLCP, Optimization 67, 2031-2060 (2018)

Bai, Y.Q., El Ghami, M., Roos, C.: A comparative study of kernel functions for primal-dual interior-point
algorithms in linear optimization. SIAM J. Optim. 15, 101128 (2004)

Chung, S.-J.: Np-completeness of the linear complementarity problem, J. Optim. Theory Appl., 60, 393-399
(1989)

Darvay, Zs.: New interior-point algorithms in linear programming, Adv. Model Optim. 5, 51-92 (2003)

Darvay, Zs.: A new predictor-corrector algorithm for linear programming, Alk. Mat. Lapok, 22, 135-161 (2005),
in Hungarian.

Darvay, Zs.: A predictor-corrector algorithm for linearly constrained convex optimization, Studia Univ. Babes-Bolyai, Ser. Informatica, 54, 121-138 (2009)

Darvay, Zs., Illés, T., Majoros, Cs.: Interior-point algorithm for sufficient LCPs based on the technique of
algebraically equivalent transformation, Optim. Lett., 15, 357-376 (2021)

Darvay, Zs., Illés, T., Povh, J., Rigó, P.R.: Predictor-corrector interior-point algorithm for sufficient linear
complementarity problems based on a new search direction, SIAM J. Optim., 30, 2628-2658 (2020)

Darvay, Zs., Papp, I.-M., Takács, P.-R.: Complexity analysis of a full-Newton Step interior-point method for
linear optimization, Period. Math. Hung., 73, 27-42 (2016)

Darvay, Zs., Rigó, P.R.: New interior-point algorithm for symmetric optimization based on a positive-asymptotic
barrier function, Numer. Funct. Anal. Optim. 39, 1705-1726 (2018)

Faraut, J., Korányi, A.: Analysis on Symmetric Cones, Oxford Mathematical Monographs. The Clarendon Press
Oxford University Press, New York, Oxford Science Publications (1994)

Faybusovich, L.: Linear systems in Jordan algebras and primal-dual interior-point algorithms, J. Comput. Appl.
Math. 86, 149-175 (1997)

Güler, O.: Barrier functions in interior point methods, Math. Oper. Res. 21, 860-885 (1996)

Karimi, M., Luo, S., Tun�cel, L.: Primal-dual entropy-based interior-point algorithms for linear optimization,
RAIRO-Oper. Res. 51, 299-328 (2017)

Karmarkar, N.K.: A new polynomial-time algorithm for linear programming, Combinatorica 4, 373-395 (1984)

Kheirfam, B., Haghighi, M.: A full-newton step feasible interior-point algorithm for P_*(κ)-LCP based on a new
search direction, Croat. Oper. Res. Rev. 7, 277-290 (2016)

Kojima, M., Megiddo, N., Noma, T. , Yoshise, A.: A unified approach to interior point algorithms for linear
complementarity problems, Lecture Notes in Comput. Sci. 538, Springer-Verlag, New York (1991)

Lesaja, G., Roos, C.: Unified analysis of kernel-based interior-point methods for P_*(κ)-LCP, SIAM J. Optim.
21, 2994-3013 (2011)

Luo, Z., Xiu, N.: Path-following interior point algorithms for the Cartesian P_*(κ)-LCP over symmetric cones, Science in China Series A: Mathematics 52, 1769-1784 (2009)

Mohammadi, N., Mansouri, H., Zangiabadi, M., Asadi, S.: A full Nesterov-Todd step infeasible-interior-point
algorithm for Cartesian P_*(κ) horizontal linear complementarity problem over symmetric cones, Optimization
65, 539-565 (2015)

Nesterov, Y.E., Todd, M.J.: Self-scaled barriers and interior-point methods for convex programming, Math.
Oper. Res. 22, 1-42 (1997)

Nesterov, Y.E., Todd, M.J.: Primal-dual interior-point methods for self-scaled cones, SIAM J. Optim. 8, 324-364
(1998)

Pan, S., Li, X., He, S.: An infeasible primal-dual interior point algorithm for linear programs based on logarithmic
equivalent transformation, J. Math. Anal. Appl. 314, 644-660 (2006)

Rigó, P.R.: New trends in algebraic equivalent transformation of the central path and its applications, PhD
thesis, Budapest University of Technology and Economics, Institute of Mathematics, Hungary (2020)

Rigó, P.R.: New trends in interior-point algorithms, In F. Friedler ed., Proceeding of the 8th VOCAL Optimization
Conference: Advanced Algorithms (short papers), Esztergom, Hungary, 85-90 (2018)

Rigó, P.R., Darvay, Zs.: Infeasible interior-point method for symmetric optimization using a positive-asymptotic
barrier, Comput. Optim. Appl. 71, 483-508 (2018)

Peng, J., Roos, C., Terlaky, T.: Self-Regularity, A New Paradigm for Primal-Dual Interior-Point Algorithms,
Princeton University Press, Princeton, NJ (2002)

Roos, C., Terlaky, T., Vial, J.Ph.: Theory and Algorithms for Linear Optimization, Springer, New York (2005)
20

Schmieta, S.H., Alizadeh, F.: Extension of primal-dual interior point algorithms to symmetric cones, Math.
Program. 96, 409-438 (2003)

Sturm, J.F.: Similarity and other spectral relations for symmetric cones, Linear Algebra Appl. 312, 135-154
(2000)

Tuncel, L., Todd, M.J.: On the interplay among entropy, variable metrics and potential functions in interior-point
algorithms, Comput. Optim. Appl. 8, 5-19 (1997)

Vieira, M.V.C.: Jordan algebraic approach to symmetric optimization, PhD thesis, Delf University of Technology,
The Netherlands (2007)

Wang, G.Q., Bai, Y.Q.: A new full Nesterov-Todd step primal-dual path-following interior-point algorithm for
symmetric optimization, J. Optim. Theory Appl. 154, 966-985 (2012)

Wright, S.: Primal-Dual Interior-Point Methods, SIAM, Philadelphia (1997)

Ye, Y.: Interior Point Algorithms, Theory and Analysis. Wiley, Chichester (1997)