Sun, Hongchun; Wang, Yiju Further discussion on the error bound for generalized linear complementarity problem over a polyhedral cone. (English) Zbl 1288.90112 J. Optim. Theory Appl. 159, No. 1, 93-107 (2013). Authors’ abstract: We consider the global error bound for the generalized linear complementarity problem over a polyhedral cone (GLCP). Based on the new transformation of the problem, we establish its global error bound under milder conditions, which improves the result obtained by [H. C. Sun et al., J. Optim. Theory Appl. 142, No. 2, 417–429 (2009; Zbl 1190.90243)] for GLCP by weakening the assumption. Reviewer: Shmuel Gal (Haifa) Cited in 12 Documents MSC: 90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) Keywords:GLCP; reformulation; global error bound Citations:Zbl 1190.90243 PDFBibTeX XMLCite \textit{H. Sun} and \textit{Y. Wang}, J. Optim. Theory Appl. 159, No. 1, 93--107 (2013; Zbl 1288.90112) Full Text: DOI References: [1] Andreani, R., Friedlander, A., Santos, S.A.: On the resolution of the generalized nonlinear complementarity problem. SIAM J. Optim. 12, 303-321 (2001) · Zbl 1006.65068 · doi:10.1137/S1052623400377591 [2] Wang, Y.J., Ma, F.M., Zhang, J.Z.: A nonsmooth L-M method for solving the generalized nonlinear complementarity problem over a polyhedral cone. Appl. Math. Optim. 52(1), 73-92 (2005) · Zbl 1087.65064 · doi:10.1007/s00245-005-0823-4 [3] Zhang, X.Z., Ma, F.M., Wang, Y.J.: A Newton-type algorithm for generalized linear complementarity problem over a polyhedral cone. Appl. Math. Comput. 169, 388-401 (2005) · Zbl 1080.65052 · doi:10.1016/j.amc.2004.09.057 [4] Facchinei, F., Pang, J.S.: Finite-Dimensional Variational Inequality and Complementarity Problems. Springer, New York (2003) · Zbl 1062.90002 [5] Pang, J.S.: Error bounds in mathematical programming. Math. Program. 79, 299-332 (1997) · Zbl 0887.90165 [6] Sun, H.C., Wang, Y.J., Qi, L.Q.: Global error bound for the generalized linear complementarity problem over a polyhedral cone. J. Optim. Theory Appl. 142, 417-429 (2009) · Zbl 1190.90243 · doi:10.1007/s10957-009-9509-4 [7] Mangasarian, O.L.: Error bounds for nondegenerate monotone linear complementarity problems. Math. Program. 48, 437-445 (1990) · Zbl 0716.90094 · doi:10.1007/BF01582267 [8] Horn, R.A., Johnson, C.R.: Topics in Matrix Analysis. Cambridge University Press, Cambridge (1991) · Zbl 0729.15001 · doi:10.1017/CBO9780511840371 [9] Xiu, N.H., Zhang, J.Z.: Global projection-type error bound for general variational inequalities. J. Optim. Theory Appl. 112(1), 213-228 (2002) · Zbl 1005.49004 · doi:10.1023/A:1013056931761 [10] Hoffman, A.J.: On the approximate solutions of linear inequalities. J. Res. Natl. Bur. Stand. 49(4), 263-265 (1952) · doi:10.6028/jres.049.027 [11] Yamashita, N., Fukushima, M.: On the rate of convergence of the Levenberg-Marquardt method. Computing, Suppl. 15, 237-249 (2001) · Zbl 1001.65047 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.