Infeasible path-following interior point algorithm for Cartesian P_*(κ) nonlinear complementarity problems over symmetric cones

References

• B.H. Ahn, Iterative methods for linear complementarity problem with upperbounds and lower-bounds, Math. Program. 26 (1983), pp. 265–315.
   Web of Science ®Google Scholar
• 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), pp. 400–417. doi: 10.1137/040604492
   Web of Science ®Google Scholar
• E. Andersen and Y. Ye, On a homogeneous algorithm for the monotone complementarity problems, Math. Program. 84 (1999), pp. 375–400. doi: 10.1007/s101070050027
   Web of Science ®Google Scholar
• X. Chen and H.D. Qi, Cartesian P-property and its applications to the semidefinite linear complementarity problem, Math. Program. 106 (2006), pp. 177–201. doi: 10.1007/s10107-005-0601-8
   Web of Science ®Google Scholar
• J. Faraut and A. Kornyi, Analysis on Symmetric Cone, Oxford University Press, New York, 1994.
   Google Scholar
• Y. Fathi, Computational complexity of LCPs associated with positive definite matrices, Math. Program. 17 (1979), pp. 335–344. doi: 10.1007/BF01588254
   Web of Science ®Google Scholar
• L. Faybusovich, Linear systems in Jordan algebras and primal-dual interior-point algorithms, J. Comput. Appl. Math. 86 (1997), pp. 149–175. doi: 10.1016/S0377-0427(97)00153-2
   Web of Science ®Google Scholar
• L.C. Kong, L. Tuncel, and N.H. Xiu, Vector-valued implicit lagrangian for symmetric cone complementarity problems, Research Report CORR 2006-24, Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, Canada, 2006.
   Google Scholar
• G. Lesaja and C. Roos, Kernel-based interior-point methods for monotone linear complementarity problems over symmetric cones, J. Optim. Theory Appl. 150 (2011), pp. 444–474. doi: 10.1007/s10957-011-9848-9
   Web of Science ®Google Scholar
• G. Lesaja, G.Q. Wang, and D.T. Zhu, Interior-point methods for Cartesian P∗(κ)-linear complementarity problems over symmetric cones based on the eligible kernel functions, Optim. Methods Softw. 27(4–5) (2012), pp. 827–843. doi: 10.1080/10556788.2012.670858
   Web of Science ®Google Scholar
• H. Liu, X. Liu, and C. Liu, Mehrotra-type predictor-corrector algorithms for sufficient linear complementarity problem, Appl. Numer. Math. 62 (2012), pp. 1685–1700. doi: 10.1016/j.apnum.2012.05.009
   Web of Science ®Google Scholar
• H. Liu, X. Liu, and C. Liu, Infeasible Mehrotra-type predictor-corrector interior-point algorithm for the Cartesian P∗(κ)-LCP over symmetric cones, Numer. Funct. Anal. Optim. 35(5) (2014), pp. 588–610. doi: 10.1080/01630563.2013.836107
   Web of Science ®Google Scholar
• X. Liu, H. Liu, and W. Wang, Polynomial convergence of Mehrotra-type predictor corrector algorithm for the Cartesian P∗(κ) -LCP over symmetric cones, Optimization 64(4) (2013), pp. 1–23. doi: 10.1155/2013/197370
   Web of Science ®Google Scholar
• H. Liu, X. Yang, and C. Liu, A new wide neighborhood primal dual infeasible interior point method for symmetric cone programming, J. Optim. Theory Appl. 158 (2013), pp. 796–815. doi: 10.1007/s10957-013-0303-y
   Web of Science ®Google Scholar
• Z. Luo and N. Xiu, An infeasible interior-point algorithm for symmetric cone LCP via CHKS function, Acta Appl. Math. 25 (2009), pp. 593–606. doi: 10.1007/s10255-008-8814-2
   Web of Science ®Google Scholar
• Z. Luo and N. Xiu, Path-following interior point algorithms for the Cartesian P∗(κ) -LCP over symmetric cones, Sci. China Ser. A 52 (2009), pp. 1769–1784. doi: 10.1007/s11425-008-0174-0
   Google Scholar
• M. Muramatsu, On commutative class of search directions for linear programming over symmetric cones, J. Optim. Theory Appl. 112 (2002), pp. 595–625. doi: 10.1023/A:1017920200889
   Web of Science ®Google Scholar
• K.G. Murty, Linear complementarity, linear and nonlinear programming, Sigma Ser. Appl. Math. 3, Heldermann-Verlag: Berlin, 1998.
   Google Scholar
• B. Rangarajan, Polynomial convergence of infeasible-interior-point methods over symmetric cones, SIAM J. Optim. 16 (2006), pp. 1211–1229. doi: 10.1137/040606557
   Web of Science ®Google Scholar
• S.H. Schmieta and F. Alizadeh, Extension of primal-dual interior-point algorithm to symmetric cones, Math. Program. 96 (2003), pp. 409–438. doi: 10.1007/s10107-003-0380-z
   Web of Science ®Google Scholar
• G.Q. Wang and Y.Q. Bai, A class of polynomial interior point algorithms for the cartesian p-matrix linear complementarity problem over symmetric cones, J. Optim. Theory Appl. 152 (2012), pp. 739–772. doi: 10.1007/s10957-011-9938-8
   Web of Science ®Google Scholar
• A. Yoshise, Interior point trajectories and a homogeneous model for nonlinear complementarity problem over symmetric cones, SIAM J. Optim. 17 (2006), pp. 1129–1153. doi: 10.1137/04061427X
   Web of Science ®Google Scholar
• A. Yoshise, Homogenous algorithms for monotone complementarity problems over symmetric cones, Pac. J. Optim. 5(2) (2008), pp. 313–337.
   Web of Science ®Google Scholar
• A. Yoshise, Complementarity problems over symmetric cones, Discussion Paper Series, No. 1262, University of Tsukuba, Tsukuba, Japan, 2010.
   Google Scholar
• J. Zhang and K. Zhang, Polynomial complexity of an interior point algorithm with a second order corrector step for symmetric cone programming, Math. Methods Oper. Res. 73 (2011), pp. 75–90. doi: 10.1007/s00186-010-0334-1
   Web of Science ®Google Scholar
• Y.B. Zhao and J.Y. Han, Two interior point methods for nonlinear P∗(κ)- complementarity problem, J. Optim. Theory Appl. 102(3) (1999), pp. 659–679. doi: 10.1023/A:1022606324827
   Google Scholar