A non-interior predictor-corrector path following algorithm for the monotone linear complementarity problem

Mathematical Programming, Series B

Volumn 87, Issue 1, 2000, Pages 113-130

  Burke, Jim ^a   Xu, Song ^b  

^a UNIVERSITY OF WASHINGTON   (United States)

^b UNIVERSITY OF WATERLOO   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000555874     PISSN: 00255610     EISSN: None     Source Type: Journal    
DOI: 10.1007/s101079900111     Document Type: Article

References (26)

1. Burke, J., Xu, S. (1998): The global linear convergence of a non-interior path-following algorithm for linear complementarity problem. Math. Oper. Res. 23, 719-734
2. Chen, B., Chen, X. (1997): A global linear and local'quadratic continuation method for variational inequalities with box constraints. Preprint, Department of Management and Systems, Washington State University, Pullman, WA 99164-4736, March 1997. To appear in Comput. Optim. Appl.
3. 0 NCP or monotone NCP. SIAM J. Optim. 9, 624-645
4. Chen, B., Harker, P. (1993): A non-interior-point continuation method for linear complementarity problems, SIAM J. Matrix Anal. Appl. 14, 1168-1190
5. Chen, B., Xiu, N. (1999): A global linear and local quadratics non-interior continuation method for nonlinear complementarity problems based on Chen-Mangasarian smoothing functions. SIAM J. Optim. 9, 605-623
6. Chen, C., Mangasarian, O.L. (1996): A class of smoothing functions for nonlinear and mixed comple-mentarity problems, Comput. Optim. Appl. 5, 97-138
7. Chen, X., Qi, L., Sun, D. (1998): Global and superlinear convergence of the smoothing newton method and its application to general box constrained variational inequalities. Math. Comput. 67, 519-540
8. Chen, X., Ye, Y. (1997): On homotopy smoothing methods for variational inequalities. AMR 96/39, Applied Mathematics Report, The University of New South Wales, Sydney, Australia
9. Fukushima, M., Luo, Z.-Q., Pang, J.-S. (1998): A globally convergent sequential quadratic programming algorithm for mathematical programs with linear complementarity constraints. Comput. Optim. Appl. 10, 5-34
10. Hotta, K., Yoshise, A. (1999): Global convergence of a class of non-interior-point algorithms using Chen-Harker-Kanzow functions for nonlinear complementarity problems. Math. Program. 86, 105-133
11. Jiang, H. (1997): Smoothed Fischer-Burmeister equation methods for the complementarity problem. Report, Department of Mathematics, University of Melbourne, Parkville, Australia
12. Jones, C., Gowda, M.S. (1998): On the connectedness of solution sets in linear complementarity problems. Linear Algebra Appl. 272, 33-44
13. Kanzow, C. (1996): Some noninterior continuation methods for linear complementarity problems, SIAM J. Matrix Anal. Appl. 17, 851-868
14. Kanzow, C. (1997): Private communications. Seattle, Washington
15. Kojima, M., Meggido, N., Noma, T., Yoshise, A. (1991): A unified approach to interior point algorithms for linear complementarity problems. Springer-Verlag, Berlin
16. Mizuno, S., Todd, M., Ye, Y. (1993): On adaptive step primal-dual interior-point algorithms for linear programming. Math. Oper. Res. 18, 964-981
17. Qi, L. (1993): Convergence analysis of some algorithms for solving nonsmooth equations, Math. Oper. Res. 18, 227-244
18. Qi, L., Sun, D. (1997): Globally linearly, and globally and locally superlinearly convergent versions of the Hotta-Yoshise non-interior point algorithm for nonlinear complementarity problems. Applied Mathematics Report, School of Mathematics University of New South Wales, Sydney 2052, Australia
19. Qi, L., Sun, D., Zhou, G. (1997): A new look at smoothing Newton methods for nonlinear complementarity problems and box constrained variational inequalities. Applied Mathematics Report, AMR 97/13, School of Mathematics University of New South Wales, Sydney 2052, Australia
20. Robinson, S. (1992): Normal maps induced by linear transformations. Math. Oper. Res. 17, 691-714
21. Smale, S. (1986): Algorithms for solving equations. Proceedings of the International Congress of Mathematicians, Berkeley, California
22. Tseng, P. (1997): An infeasible path-following method for monotone complementarity problems, SIAM J. Optim. 7, 386-402
23. Tseng, P. (1998): Analysis of a non-interior continuation method based on Chen-Mangasarian smoothing functions for complementarity problems. To appear in Fukushima, M., Qi, L., eds., Reformulation - Nonsmooth, Piecewise Smooth, Semismooth, and Smoothing Methods. Kluwer Academic Publisher, Nowell, Maryland
24. Wright, S.J. (1997): Primal-Dual Interior-Point Methods, SIAM, Philadelphia, PA
25. Xu, S. (1996): The global linear convergence of an infeasible non-interior path-following algorithm for complementarity problems with uniform P-functions. Technical Report, Department of Mathematics, University of Washington, Seattle, WA 98195, December 1996
26. Xu, S. (1997): The global linear convergence and complexity of a non-interior path-following algorithm for monotone LCP based on Chen-Harker-Kanzow-Smale smoothing function. Technical Report, Department of Mathematics, University of Washington, Seattle, WA 98195, February 1997