An infeasible interior-point algorithm based on modified Nesterov and Todd directions for symmetric linear complementarity problem

References

• Schmieta SH, Alizadeh F. Extension of primal-dual interior-point algorithm to symmetric cones. Math. Program. 2003;96:409–438.
   Web of Science ®Google Scholar
• Schmieta SH, Alizadeh F. Associative and Jordan algebras and polynomial time interior-point algorithms for symmetric cones. Math. Oper. Res. 2001;26:543–564.
   Web of Science ®Google Scholar
• Faybusovich L. Euclidean Jordan algebras and interior-point algorithms. Positivity. 1997;1:331–357.
   Web of Science ®Google Scholar
• Tseng P. Search directions and convergence analysis of some infeasible path-following methods for monotone semidefinite LCP. Optim. Methods Softw. 1998;9:245–268.
   Web of Science ®Google Scholar
• Ye Y, Pardalos PM. A class of linear complementarity problems solvable in polynomial time. Linear Algebra Appl. 1991;152:3–17.
   Web of Science ®Google Scholar
• Pardalos PM, Ye Y, Han CG, Kalinski J. Solution of p-matrix linear complementarity problems using a potential reduction algorithm. SIAM J. Matrix Anal. Appl. 1993;14:1048–1060.
   Web of Science ®Google Scholar
• Gowda MS, Sznajder R. Some global uniqueness and solvability results for linear complementarity problems over symmetric cones. SIAM J. Optim. 2007;18:461–481.
   Web of Science ®Google Scholar
• Lesaja G, Roos C. Kernel-based interior-point methods for monotone linear complementarity problems over symmetric cones. J. Optim. Theory Appl. 2011;150:444–474.
   Web of Science ®Google Scholar
• Kheirfam B, Mahdavi-Amiri N. A new interior-point algorithm based on modified Nesterov-Todd direction for symmetric cone linear complementarity problem. Optim. Lett. 2013. doi: 10.1007/s11590-013-0618-5.
   Web of Science ®Google Scholar
• Lustig IJ. Feasible issues in a primal-dual interior-point method. Math. Program. 1990;67:145–162.
   Web of Science ®Google Scholar
• Kojima M, Megiddo N, Mizuno S. A primal-dual infeasible-interior-point algorithm for linear programming. Math. Program. 1993;61:263–280.
   Web of Science ®Google Scholar
• Mizuno S. Polynomiality of infeasible-interior-point algorithms for linear programming. Math. Program. 1994;67:109–119.
   Web of Science ®Google Scholar
• Potra FA. An infeasible-interior-point predictor-corrector algorithm for linear programming. SIAM J. Optim. 1996;6:19–32.
   Web of Science ®Google Scholar
• Rangarajan BK. Polynomial convergence of infeasible-interior-point methods over symmetric cones. SIAM J. Optim. 2006;16:1211–1229.
   Web of Science ®Google Scholar
• Roos C. A full-Newton step O(n) infeasible interior-point algorithm for linear optimization. SIAM J. Optim. 2006;16:1110–1136.
   Web of Science ®Google Scholar
• Mansouri H, Roos C. A new full-Newton step O(n) infeasible interior-point algorithm for semidefinite optimization. Numer. Alg. 2009;52:225–255.
   Web of Science ®Google Scholar
• Mansouri H, Zangiabadi M, Pirhaji M. A full-Newton step O(n) infeasible-interior-point algorithm for linear complementarity problems. Nonlinear Anal.:Real. 2011;12:545–561.
   Web of Science ®Google Scholar
• Mansouri H, Siyavash T, Zangiabadi M. A path-following infeasible interior-point algorithm for semidefinite programming. Iranian J. Oper. Res. 2012;3:11–30.
   Google Scholar
• Mansouri H, Zangiabadi M. New complexity analysis of a full Nesterov--Todd steps IIPM for semidefinite optimization. Bull. Iranian Math. Soc. 2011;37:269–285.
   Web of Science ®Google Scholar
• Zangiabadi M, Mansouri H. Improved infeasible-interior-point algorithm for linear complementarity problems. Bull. Iranian Math. Soc. 2012;38:787--803.
   Web of Science ®Google Scholar
• Mansouri H, Zangiabadi M. An adaptive infeasible interior-point algorithm with full-Newton step for linear optimization. Optimization. 2013;62:285–297.
   Web of Science ®Google Scholar
• Kheirfam B, Mahdavi-Amiri N. A full Nesterov-Todd step infeasible interior-point algorithm for symmetric cone linear complementarity problem. Bull. Iranian Math. Soc. 2013, in press.
   Web of Science ®Google Scholar
• Faraut J, Korányi A. Analysis on symmetric cones. New York (NY): Oxford University Press; 1994.
   Google Scholar
• Faybusovich L. A Jordan-algebraic approach to potential-reduction algorithms. Math. Zeitschrift. 2002;239:117–129.
   Web of Science ®Google Scholar
• Sturm JF. Similarity and other spectral relations for symmetric cones. Algebra Appl. 2000;312:135–154.
   Web of Science ®Google Scholar
• Gu G, Zangiabadi M, Roos C. Full Nesterov--Todd step infeasible interior-point method for symmetric optimization. Eur. J. Oper. Res. 2011;214:473–484.
   Web of Science ®Google Scholar
• Cottle R, Pang JS, Stone RE. The linear complementarity problem. Boston (MA):Academic Press; 1992.
   Google Scholar
• Harker P, Pang J. A damped-Newton method for the linear complementarity problem. In: Allgower G, Georg K, editors. Simulation and optimization of large systems. Vol. 26, Lectuers in applied mathematics. Providence (RI): American Mathematical Society; 1990. p. 265–284.
   Google Scholar