Error bounds for R0-type and monotone nonlinear complementarity problems

Journal of Optimization Theory and Applications

Volumn 108, Issue 2, 2001, Pages 297-316

  Chen, B ^a  

^a WASHINGTON STATE UNIVERSITY   (United States)

Author keywords

Complementarity problems; Error bounds; R0 functions

Indexed keywords

COMPLEMENTARITY PROBLEMS; ERROR BOUND; GLOBAL ERROR BOUND; LINEAR COMPLEMENTARITY PROBLEMS; LOCAL ERROR BOUND; MATRIX; MONOTONE FUNCTIONS; NONLINEAR COMPLEMENTARITY PROBLEM; R0-FUNCTION;

ERROR ANALYSIS;

EID: 0035529806     PISSN: 00223239     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1026434200384     Document Type: Article

References (22)

1. 1. MANGASARIAN, O. L., and REN, J., New Improved Error Bounds for the Linear Complementarity Problem, Mathematical Programming, Vol. 66, pp. 241-255, 1994.
2. 2. TSENG, P., Growth Behavior of a Class of Merit Functions for the Nonlinear Complementarity Problem, Journal of Optimization Theory and Applications, Vol. 89, pp. 17-37, 1996.
3. 3. TSENG, P., YAMASHITA, N., and FUKUSHIMA, M., Equivalence of Complementarity Problems to Differentiable Minimization: A Unified Approach, SIAM Journal of Optimization, Vol. 6, pp. 446-460, 1996.
4. 4. LUO, Z. Q., and TSENG, P., Error Bound and Convergence Analysis of Matrix Splitting Algorithms for the Affine Variational Inequality Problem, SIAM Journal on Optimization, Vol. 2, pp. 43-54, 1992.
5. 5. LUO, Z. Q., MANGASARIAN, O. L., REN, J., and SOLODOV, M. V., New Error Bounds for the Linear Complementarity Problem, Mathematics of Operations Research, Vol. 19, pp. 880-892, 1994.
6. 6. ROBINSON, S. M., Some Continuity Properties of Polyhedral Multifunctions, Mathematical Programming Study, Vol. 14, pp. 206-214, 1981.
7. 7. MATHIAS, R., and PANG, J. S., Error Bounds for the Linear Complementarity Problem with a P-Matrix, Linear Algebra and Applications, Vol. 132, pp. 123-136, 1990.
8. 8. MANGASARIAN, O. L., and SHIAU, T. H., Error Bounds for Monotone Linear Complementarity Problems, Mathematical Programming, Vol. 36, pp. 81-89, 1986.
9. 9. LI, W., Error Bounds for Piecewise Quadratic Programs and Applications, SIAM Journal on Control and Optimization, Vol. 33, pp. 1510-1529, 1995.
10. 10. LUO, Z. Q., and PANG, J. S., Error Bounds for Analytic Systems and Their Applications, Mathematical Programming, Vol. 67, pp. 1-28, 1994.
11. 11. KANZOW, C., YAMASHITA, N., and FUKUSHIMA, M., New NCP-Functions and Their Properties, Journal of Optimization Theory and Applications, Vol. 94, pp. 115-135, 1997.
12. 12. CHEN, B., and HARKER, P. T., Smoothing Approximations to Nonlinear Complementarity Problems, SIAM Journal on Optimization, Vol. 7, pp. 403-420, 1997.
13. 13. KANZOW, C., and FUKUSHIMA, M., Equivalence of the Generalized Complementarity Problem to Differentiable Unconstrained Minimization, Journal of Optimization Theory and Applications, Vol. 90, pp. 581-603, 1996.
14. 14. LUO, Z. Q., and TSENG, P., A New Class of Merit Functions for the Nonlinear Complementarity Problem, Complementarity and Variational Problems: State of the Art, Edited by M. C. Ferris and J. S. Pang, SIAM Publications, pp. 204-225, 1997.
15. 15. PANG, J. S., Inexact Newton Methods for the Nonlinear Complementarity Problem, Mathematical Programming, Vol. 36, pp. 54-71, 1986.
16. 16. PANG, J. S., Error Bounds in Mathematical Programming, Mathematical Programming, Vol. 79, pp. 299-332, 1997.
17. 17. TSENG, P., An Infeasible Path-Following Method for Monotone Complementarity Problems, SIAM Journal on Optimization, Vol. 7, pp. 386-402, 1997.
18. 18. CHEN, B., CHEN, X., and KANZOW, C., A Penalized Fischer-Burmeister NCP-Function, Mathematical Programming (to appear).
19. 19. MANGASARIAN, O. L., and REN, J., New Error Bounds for the Nonlinear Complementarity Problem, Communications on Applied Nonlinear Analysis, Vol. 1, pp. 49-56, 1994.
20. 20. PANG, J. S., and QI, L., Nonsmooth Equations: Motivation and Algorithms, SIAM Journal on Optimization, Vol. 3, pp. 443-465, 1993.
21. 0 Nonlinear Complementarity Problems, Mathematics of Operations Research, Vol. 23, pp. 735-745, 1998.
22. 22. CHEN, X., and YE, Y., On Homotopy-Smoothing Methods for Variational Inequalities, SIAM Journal on Control and Optimization, Vol. 37, pp. 589-616, 1999.