Verification for existence of solutions of linear complementarity problems

Linear Algebra and Its Applications

Volumn 324, Issue 1-3, 2001, Pages 15-26

  Chen, Xiaojun ^a   Shogenji, Yukihiro ^b   Yamasaki, Maretsugu ^a  

^a SHIMANE UNIVERSITY   (Japan)

^b EHIME UNIVERSITY   (Japan)

Author keywords

Linear complementarity problems; Numerical validation; P0 matrix

Indexed keywords

EID: 0035587726     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0024-3795(99)00272-4     Document Type: Article

References (20)

1. Ahn B.H. Iterative methods for linear complementarity problem with upperbounds and lowerbounds. Math. Programming. 26:1983;265-315.
2. Alefeld G., Chen X., Potra F. Numerical validation of solutions of linear complementarity problems. Numer. Math. 83:1999;1-23.
3. Alefeld G., Gienger A., Potra F. Efficient numerical validation of solutions of nonlinear systems. SIAM J. Numer. Anal. 31:1994;252-260.
4. J. Burke, S. Xu, The global linear convergence of a non-interior path-following algorithm for linear complementarity problem, Math. Oper. Res. 23 (1998) 719-734.
5. Chen B., Harker P.T. A non-interior-point continuation method for linear complementarity problems. SIAM J. Matrix Anal. Appl. 14:1993;1168-1190.
6. Chen C., Mangasarian O.L. Smoothing methods for convex inequalities and linear complementarity problems. Math. Programming. 71:1995;51-69.
7. Chen X. A verification method for solutions of nonsmooth equations. Computing. 58:1997;281-294.
8. Chen X., Ye Y. On homotopy-smoothing methods for box-constrained variational inequalities. SIAM J. Control Optim. 37:1999;587-616.
9. R.W. Cottle, J.S. Pang, R.E. Stone, The Linear Complementarity Problem, Academic Press, Boston, 1992.
10. Fathi Y. Computational complexity of LCPs associated with positive definite matrices. Math. Programming. 17:1979;335-344.
11. Frommer A., Mayer G. A new criterion to guarantee the feasibility of the interval Gaussian algorithm. SIAM J. Matrix Anal. Appl. 14:1993;408-419.
12. S. Gabriel, J. Moré, Smoothing of mixed complementarity problems, in: M.C. Ferris, J.S. Pang (Eds.), Complementarity and Variational Problems: State of the Art, SIAM, Philadelphia, 1997, pp. 105-116.
13. S.I. Gass, Linear Programming. Methods and Applications, McGraw-Hill, New York, 1975.
14. Kanzow C. Some noninterior continuation methods for linear complementarity problems. SIAMJ. Matrix Anal. Appl. 17:1996;851-868.
15. R.B. Kearfott, Rigorous Global Search: Continuous Problems, Kluwer Academic Publishers, Dordrecht, 1996.
16. K.G. Murty, Linear Complementarity, Linear and Nonlinear Programming, Heldermann, Berlin, 1988.
17. Rump S.M. Expansion and estimation of the range of nonlinear function. Math. Comp. 65:1996;1503-1512.
18. S.M. Rump, INTLAB-INTerval LABoratory, Technical report, Inst. f. Infomatik III, Technical University Hamburg, Harburg, 1998.
19. S.J. Wright, Primal-Dual Interior-Point Methods, SIAM, Philadelphia, 1996.
20. Ye Y. On homogeneous and self-dual algorithms for LCP. Math. Programming. 76:1996;211-221.