On the rate of local convergence of high-order-infeasible-path-following algorithms for P*-linear complementarity problems

Computational Optimization and Applications

Volumn 14, Issue 3, 1999, Pages 293-307

  Zhao, Gongyun ^a   Sun, Jie ^a  

^a NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTATIONAL COMPLEXITY; CONVERGENCE OF NUMERICAL METHODS; ITERATIVE METHODS; PROBLEM SOLVING;

HIGH-ORDER ALGORITHMS; INTERIOR POINT METHODS; LINEAR COMPLEMENTARITY PROBLEMS;

LINEAR PROGRAMMING;

EID: 0032595831     PISSN: 09266003     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1026492106091     Document Type: Article

References (18)

1. J.F. Bonnans and C.C. Gonzaga, "Convergence of interior point algorithms for the linear complementarity problem," Mathematics of Operations Research, vol. 21, pp. 1-25, 1996.
2. R.W. Cottle, J.-S. Pang, and R.E. Stone, The Linear Complementarity Problem, Academic Press: Boston, 1992.
3. M.S. Gowda, "On the extended linear complementarity problem," Mathematical Programming, vol. 72, pp. 33-50, 1996.
4. P. Hung and Y. Ye, "An asymptotical O(√nL)-iteration path-following linear programming algorithm that uses long steps," SIAM Journal on Optimization, vol. 6, pp. 570-586, 1996.
5. M. Kojima, N. Megiddo, T. Noma, and A. Yoshise, A Unified Approach to Interior Point Algorithms for Linear Complementarity Problems, Springer-Verlag: Berlin, 1996.
6. K. McShane, "Superlinearly convergent O(√nL)-iteration interior point algorithms for LP and the monotone LCP," SIAM Journal on Optimization, vol. 4, pp. 247-261, 1994.
7. S. Mizuno, "A superlinearly convergent infeasible-interior-point algorithm for geometrical LCPs without a strictly complementarity condition," Mathematics of Operations Research, vol. 2, pp. 382-400, 1996.
8. S. Mizuno, F. Jarre, and J. Stoer, "A unified approach to infeasible-interior-point algorithm via geometrical linear complementarity problems," J. Appl. Math. Opt., vol. 13, pp. 315-341, 1996.
9. R. Monteiro, I. Adler, and M. Resende, "A polynomial-time primal-dual affine scaling algorithm for linear and convex quadratic programming and its power series extension," Mathematics of Operations Research, vol. 15, pp. 191-214, 1990.
10. R. Monteiro and T. Tsuchiya, "Limiting behavior of the derivatives of certain trajectories associated with a monotone horizontal linear complementarity problem," Mathematics of Operations Research, vol. 21, pp. 793-814, 1996.
11. F.A. Potra and R. Sheng, "A superlinearly convergent infeasible-interior-point algorithm for degenerate LCP," Technical Report, Dept. of Math., The University of Iowa, USA, 1995.
12. J. Stoer and M. Wechs, "Infeasible-interior-point paths for sufficient linear complementarity problems and their analyticity," Mathematical Programming, vol. 83, pp. 407-423, 1998.
13. J. Stoer, M. Wechs, and S. Mizuno, "High order infeasible-interior-point methods for solving sufficient linear complementarity problems," Mathematics of Operations Research, vol. 23, pp. 832-862, 1998.
14. J.F. Sturm, "Superlinear convergence of an algorithm for monotone linear complementarity problems, when no strictly complementary solution exists," Mathematics of Operations Research, vol. 24, pp. 72-94, 1999.
15. H. Väliaho, "P*-matrices are just sufficient," Linear Algebra and Its Applications, vol. 239, pp. 103-108, 1996.
16. S.J. Wright and Y. Zhang, "A superquadratic infeasible-interior-point method for linear complementarity problems," Mathematical Programming, vol. 73, pp. 269-289, 1996.
17. Y. Ye and K. Anstreicher, "On quadratic and O(√nL) convergence of a predictor-corrector algorithm for LCP," Mathematical Programming, vol. 62, pp. 537-551, 1993.
18. G. Zhao, "Interior point algorithms for linear complementarity problems based on large neighborhoods of the central path," SIAM Journal on Optimization, vol. 8, pp. 397-413, 1998.