Superlinear convergence of an algorithm for monotone linear complementarity problems, when no strictly complementary solution exists

Mathematics of Operations Research

Volumn 24, Issue 1, 1999, Pages 72-94

  Sturm, Jos F ^a  

^a MAASTRICHT UNIVERSITY   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; ASYMPTOTIC STABILITY; CONVERGENCE OF NUMERICAL METHODS; ERROR ANALYSIS; LINEAR PROGRAMMING; PROBLEM SOLVING; THEOREM PROVING;

MONOTONE LINEAR COMPLEMENTARY PROBLEMS; PREDICTOR-CORRECTOR INTERIOR POINT ALGORITHMS; TAPIA-TYPE INDICATORS;

OPERATIONS RESEARCH;

EID: 0033077428     PISSN: 0364765X     EISSN: None     Source Type: Journal    
DOI: 10.1287/moor.24.1.72     Document Type: Article

References (37)

1. Bonnans, J. F., C. C. Gonzaga. 1996. Convergence of interior point algorithms for the linear complementarity problem. Math. Oper. Res. 21 1-25.
2. _, _. 1997. Fast convergence of the simplified largest step path following algorithm. Math. Programming 76 95-115.
3. Cottle, R. W., J.-S. Pang, R. E. Stone. 1992. The linear complementarity problem, Computer science and scientific computing. Academic Press, Boston.
4. El-Bakry, A. S., R. A. Tapia, Y. Zhang. 1994. A study of indicators for identifying zero variables in interior-point methods. SIAM Rev. 36 45-72.
5. _, _, _. 1996. On the convergence rate of Newton interior point methods in the absence of strict complementarity. Computational Optimization and Applications 6 157-167.
6. Gonzaga, C. C. 1994. Interior path following algorithms. J. R. Birge and K. G. Murty, ed., Math. Programming, State of the Art 1994, University of Michigan, Ann Arbor, Michigan, 93-101.
7. Güler, O. 1992. Generalized linear complementarity problems and interior point algorithms for their solutions, Faculty of Technical Mathematics and Computer Science, TU Delft, The Netherlands. Revised 1993.
8. _, Y. Ye. 1993. Convergence behavior of interior-point algorithms. Math. Programming 60 215-228.
9. Ji, J., F. A. Potra. 1996. Tapia indicators and finite termination of infeasible-interior-point methods for degenerate LCP. The mathematics of numerical analysis, volume 32, AMS, Providence, RI, 443-454.
10. _, _, S. Huang. 1995. A predictor-corrector method for linear complementarity problems with polynomial complexity and superlinear convergence. J. Optim. Theory Appl. 84 187-199.
11. Kojima, M., N. Megiddo, T. Noma, A. Yoshise. 1991. A Unified Approach to Interior Point Algorithms for Linear Complementarity Problems. Springer-Verlag, Berlin, Germany.
12. _, S. Mizuno, T. Noma. 1990. Limiting behavior of trajectories by a continuation method for monotone complementarity problems. Math. Oper. Res. 15 662-675.
13. _, _, A. Yoshise. 1989. A polynomial-time algorithm for a class of linear complementarity problems. Math. Programming 44 1-26.
14. Luo, Z.-Q., J.-S. Pang. 1994. Error bounds for analytic systems and their applications. Math. Programming 67 1-28.
15. Mangasarian, O. L., T.-H. Shiau. 1986. Error bounds for monotone linear complementarity problems. Math. Programming 36 81-89.
16. McShane, K. 1994. Superlinearly convergent O (√nL)-iteration interior-point algorithms for LP and the monotone LCP. SIAM J. Optim. 4 247-261.
17. Mehrotra, S. 1992. On the implementation of a primal-dual interior point method. SIAM J. Optim. 2 575-601.
18. Mizuno, S. 1996. A superlinearly convergent infeasible-interior-point algorithm for geometrical LCPs without a strictly complementarity condition. Math. Oper. Res. 2 382-400.
19. _, M. J. Todd, Y. Ye. 1993. On adaptive-step primal-dual interior-point algorithms for linear programming. Math. Oper. Res. 18 964-981.
20. Monteiro, R. D. C., I. Adler, M. G. C. Resende. 1990. A polynomial-time primal-dual affine scaling algorithm for linear and convex quadratic programming and its power series extension. Math. Oper. Res. 15 191-214.
21. _, T. Tsuchiya. 1996. Limiting behavior of the derivatives of certain trajectories associated with a monotone horizontal linear complementarity problem. Math. Oper. Res. 21 793-814.
22. _, S. Wright. 1993. Local convergence of interior-point algorithms for degenerate monotone LCP. Comput. Optim. Appl. 3 131-155.
23. Murty, K. G. 1988. Linear complementarity, linear and nonlinear programming, Heldermann Verlag, Berlin, Germany.
24. Potra, F. A., R. Sheng. 1995a. A path following method for LCP with superlinearly convergent iteration sequence, Department of Mathematics, University of Iowa, Iowa City.
25. _, R. Sheng. 1995b. A superlinearly convergent infeasible-interior-point algorithm for degenerate LCP, Department of Mathematics, University of Iowa, Iowa City, Iowa.
26. 0-functions in box variational inequality problems, Department of Mathematics and Statistics, University of Maryland Baltimore County, Baltimore, Maryland.
27. Stoer, J., M. Wechs, and S. Mizuno. 1997. High order infeasible-interior-point methods for solving sufficient linear complementarity problems, Technical Report 634, The institute of statistical mathematics, Tokyo, Japan.
28. Sturm, J. F. 1998. An application of Carver's theorem to monotone linear complementarity problems, Communications Research Laboratory, McMaster University, Hamilton, Ontario.
29. _, S. Zhang. 1997. On a wide region of centers and primal-dual interior point algorithms for linear programming. Math. Oper. Res. 22 408-431.
30. 0- and P-properties; extended vorticity and horizontal LCPs. Linear Algebra Appl. 233/224 716-720. Special issue dedicated to M. Fiedler and V. Ptak.
31. Tapia, R. A. 1980. On the role of slack variables in quasi-Newton methods for constrained optimization. Numerical Optimization of Dynamic Systems, North-Holland, Amsterdam, 234-246.
32. Wright, S. J., Y. Zhang. 1996. A superquadratic infeasible-interior-point method for linear complementarity problems. Math. Programming 73 269-289.
33. _ (1994). An infeasible-interior-point algorithm for linear complementarity problems. Math. Programming 67 29-51.
34. Ye, Y. 1997. On homogeneous and self-dual algorithms for LCP. Math. Programming 76 211-221.
35. _, K. Anstreicher. 1993. On quadratic and O (√nL) convergence of a predictor-corrector algorithm for LCP. Math. Programming 62 537-551.
36. Zhang, Y., D. Zhang. 1995. On polynomiality of the Mehrotra-type predictor-corrector interior-point algorithms. Math. Programming 68 303-318.
37. *-LCP with or without strictly complementary solutions, Department of Mathematics, National University of Singapore, Singapore.