Numerical validation of solutions of complementarity problems: The nonlinear case

Numerische Mathematik

Volumn 92, Issue 1, 2002, Pages 1-16

  Alefeld, G E ^a   Chen, X ^b   Potra, F A ^c  

^a UNIVERSITY OF KARLSRUHE   (Germany)

^b SHIMANE UNIVERSITY   (Japan)

^c UNIVERSITY OF MARYLAND BALTIMORE COUNTY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036022634     PISSN: 0029599X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002110100351     Document Type: Article

References (31)

1. G. E. Alefeld, Bounding the slopes of polynomial operators and some applications. Computing 26, 227-237 (1981)
2. G. E. Alefeld, X. Chen, F. A. Potra, Numerical validation of solutions of linear complementarity problems. Numer. Math. 83, 1-23 (1999)
3. G. E. Alefeld, A. Gienger, F. A. Potra, Efficient numerical validation of solutions of nonlinear systems. SIAM J. Numer. Anal. 31, 252-260 (1994)
4. G. E. Alefeld, J. Herzberger, Introduction to Interval Computations, Academic Press, New York and London, 1983
5. E.D. Andersen, Y. Ye, A computational study of the homogeneous algorithm for large-scale convex optimization. Comput. Optim. Appl. 10, 243-280 (1988)
6. E.D. Andersen, Y. Ye, On a homogeneous algorithm for the monotone complementarity problem. Math. Programming 84, 375-399 (1999)
7. S.C. Billups, S.P. Dirkse, M.C. Ferris, A comparison of large scale mixed complementarity problem solvers. Comput. Optim. Appl. 7, 3-25 (1997) nonlinear
8. X. Chen, A verification method for solutions of nonsmooth equations. Computing 58, 281-294 (1997)
9. X. Chen, Smoothing methods for complementarity problems and their applications: a survey. J. Oper. Res. Soc. Japan 43, 32-47 (2000)
10. X. Chen, Y. Shogenji, M. Yamasaki, Verification for existence of solutions of linear complementarity problems, to appear in Linear Algebra Appl
11. F. H. Clarke, Optimization and Nonsmooth Analysis, Jonh Wiley & Sons, Inc., New York, 1983
12. M. C. Ferris, J. S. Pang, eds., Complementarity problems: State of the art, SIAM Publications, Philadelphia, 1997
13. M. Fiedler, V. Pták, Some generalization of positive definiteness and monotonicity. Numer. Math. 9, 163-172 (1966)
14. A. Frommer, G. Mayer, On the R-order of Newton-like methods for enclosing solutions of nonlinear equations. SIAM J. Numer. Anal. 27, 105-116 (1990)
15. S. Gabriel, J. More, Smoothing of mixed complementarity problems, in: M.C. Ferris and J.S. Pang, eds., Complementarity and Variational Problems: State of the Art, SIAM, Philadelphia, Pennsylvania, (1997), 105-116
16. D. Gale, H. Nikaido, The Jacobian matrix and global univalence of mappings. Math. Annalen 159, 81-93 (1965)
17. R. Hammer, M. Hocks, U. Kulisch, D. Ratz, Numerical Toolbox for Verified Computing I., Springer Verlag, Berlin, 1993
18. E. Hansen, Global Optimization Using Interval Analysis, Marcel Dekker, Inc., New York, 1992
19. R. B. Kearfott, Rigorous Global Search: Continuous Problems, Kluwer Academic Publishers, Dordrecht, 1996
20. C.T. Kelley, E.W. Sachs, Multilevel algorithms for constrained compact fixed point problems. SIAM J. Sci. Comput. 15, 645-667 (1994)
21. R. Klatte, U. Kulisch, M. Neaga, Ch. Ullrich, PASCAL-XSC - Language Reference with Examples. Springer-Verlag, Berlin, 1992
22. R. Krawczyk, A. Neumaier Interval slopes for retional functions and associated centered forms. SIAM J. Numer. Anal. 22, 604-616 (1985)
23. J. Moré, W. Rheinboldt, On P- and S- functions and related classes of n-dimensional nonlinear mappings. Linear Algebra Appl. 6 45-68 (1973)
24. J. S. Pang, L. Qi, Nonsmooth equations: motivation and algorithms. SIAM J. Optim. 3 443-465 (1993)
25. F. A. Potra, Y. Ye. Interior-point methods for nonlinear complementarity problems. J. Optim. Theory Appl. 88, 617-647 (1996)
26. S. M. Rump, Verification methods for dense and sparse systems of equations, in J. Herzberger (ed.), Topics in Validated Computations - Studies in Computational Mathematics, Elsevier, Amsterdam, 1994, pp. 63-136
27. S. M. Rump, Expansion and estimation of the range of nonlinear functions. Math. Comp. 65, 1503-1512 (1996)
28. G. W. Stewart, The efficient generation of random orthogonal matrixes with an application to condition estimators. SIAM J. Numerical Analysis 17, 403-409 (1980)
29. 0 properties in nonsmooth functions, Research Report, Department of Mathematics and Statistics, University of Maryland, Baltimore County, Baltimore, Maryland 21250, 1998
30. S. J. Wright, Primal-Dual Interior-Point Methods, SIAM Publications, Philadephia, 1997
31. Y. Ye, Interior Point Algorithms: Theory and Analysis. Wiley-Interscience Series in Discrete Mathematics and Optimization. John Wiley and Sons, 1997