zbMATH — the first resource for mathematics

A smoothing Gauss-Newton method for the generalized HLCP. (English) Zbl 0985.65070
The authors present a smoothing Gauss-Newton method for solving the generalized horizontal linear complementarity problem (HLCP) and prove that the method is both globally and locally convergent under reasonable assumptions. As a consequence, a sufficient condition for the existence and boundedness of the solutions to the problem is obtained.

65K05 Numerical mathematical programming methods
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
90C55 Methods of successive quadratic programming type
Full Text: DOI
[1] Billups, S.C.; Ferris, M.C., Convergence of an infeasible interior point algorithm from arbitrary positive starting points, SIAM J. optim., 6, 316-325, (1996) · Zbl 0854.90135
[2] Bonnans, J.F.; Gonzaga, C.C., Convergence of interior point algorithms for the monotone linear complementarity problem, Math. oper. res., 21, 1-25, (1996) · Zbl 0846.90109
[3] Burke, J.; Xu, S., The global linear convergence of a non-interior path-following algorithm for linear complementarity problem, Math. oper. res., 23, 719-734, (1998) · Zbl 0977.90056
[4] Burke, J.; Xu, S., A non-interior predictor – corrector path-following algorithm for the monotone linear complementarity problem, Math. programming, 87, 113-130, (2000) · Zbl 1081.90603
[5] Chen, B.; Xiu, N., A global linear and local quadratic non-interior continuation method for nonlinear complementarity problems based on chen – mangasarian smoothing functions, SIAM J. optim., 9, 605-623, (1999) · Zbl 1037.90052
[6] Cottle, R.W.; Pang, J.S.; Stone, R.E., The linear complementarity problem, (1992), Academic Press Boston, MA · Zbl 0757.90078
[7] Facchinei, F.; Soares, J., A new merit function for nonlinear complementarity problems and a related algorithm, SIAM J. optim., 7, 225-247, (1997) · Zbl 0873.90096
[8] Gowda, M.S., On reducing a monotone horizontal LCP to an LCP, Appl. math. lett., 8, 97-100, (1994) · Zbl 0813.65092
[9] Gowda, M.S., On the extended linear complementarity problem, Math. programming, 72, 33-50, (1996) · Zbl 0853.90109
[10] Gowda, M.S., An analysis of zero set and global error bound properties of a piecewise affine function via its recession function, SIAM J. matrix anal. appl., 17, 594-609, (1996) · Zbl 0853.90110
[11] Güler, O., Generalized linear complementarity problems, Math. oper. res., 20, 441-448, (1995) · Zbl 0837.90113
[12] H. Jiang, Smoothed Fischer-Burmeister equation methods for the complementarity problem, Report, Department of Mathematics, University of Melbourne, Parkville, Australia, June, 1997.
[13] Kanzow, C., Some noninterior continuation methods for linear complementarity problems, SIAM J. matrix anal. appl., 17, 851-868, (1996) · Zbl 0868.90123
[14] Kojima, M.; Megiddo, N.; Noma, T.; Yoshise, A., A unified approach to interior point algorithms for linear complementarity problems, lecture notes in computer science, vol. 538, (1991), Springer Berlin
[15] Mangasarian, O.L.; Pang, J.S., The extended linear complementarity problem, SIAM J. matrix anal. appl., 16, 359-368, (1995) · Zbl 0835.90103
[16] Monteiro, R.D.C.; Tsuchiya, T., Limiting behavior of the derivatives of certain trajectories associated with a monotone horizontal linear complementarity, Math. oper. res., 21, 793-814, (1996) · Zbl 0867.90111
[17] Qi, L., Convergence analysis of some algorithms for solving nonsmooth equations, Math. oper. res., 18, 227-244, (1993) · Zbl 0776.65037
[18] L. Qi, D. Sun, Smoothing functions and a smoothing Newton method for complementarity and variational inequality problems, Preprint, The University of New South Wales, Sydney 2052, Australia, October, 1998.
[19] L. Qi, D. Sun, Nonsmooth equations and smoothing methods, in: A. Eberhard, B. Glover, R. Hill, D. Ralph (Eds.), Progress in Optimization: Contributions from Australasia, Kluwer Academic Publisher, Nowell, MA, USA, 1999. · Zbl 0957.65042
[20] Qi, L.; Sun, D.; Zhou, G., A new look at smoothing Newton methods for nonlinear complementarity problems and box constrained variational inequalities, Math. programming, 87, 1-35, (2000) · Zbl 0989.90124
[21] Sznajder, R.; Gowda, M.S., Generalization of P_{0}- and P-properties; extended vertical and horizontal lcps, Linear algebra appl., 223/224, 695-715, (1995) · Zbl 0835.90104
[22] Sznajder, R.; Gowda, M.S., On the Lipschitz continuity of the solution map in some generalized linear complementarity problems, () · Zbl 0906.90165
[23] Tseng, P., Analysis of a non-interior continuation method based on Chen-Mangasarian smoothing functions for complementarity problems, (), 383-404 · Zbl 0928.65078
[24] Tütüncü, R.H.; Todd, M.J., Reducing horizontal linear complementarity problem, Linear algebra appl., 223/224, 716-720, (1995)
[25] Willson, A.N., A useful generalization of the P_{0}-matrix concept, Numer. math., 17, 62-70, (1971)
[26] Ye, Y., A fully polynomial-time approximation algorithm for computing a stationary point of the general linear complementarity problem, Math. oper. res., 18, 334-345, (1993) · Zbl 0791.90060
[27] Zhang, Y., On the convergence of a class of infeasible interior-point methods for the horizontal linear complementarity problem, SIAM J. optim., 4, 208-227, (1994) · Zbl 0803.90092
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.