Jiang, Houyuan; Fukushima, Masao; Qi, Liqun; Sun, Defeng A trust region method for solving generalized complementarity problems. (English) Zbl 0911.90324 SIAM J. Optim. 8, No. 1, 140-157 (1998). Summary: Based on a semismooth equation reformulation using Fischer’s function, a trust region algorithm is proposed for solving the generalized complementarity problem (GCP). The algorithm uses a generalized Jacobian of the function involved in the semismooth equation and adopts the squared natural residual of the semismooth equation as a merit function. The proposed algorithm is applicable to the nonlinear complementarity problem because the latter problem is a special case of the GCP. Global convergence and, under a nonsingularity assumption, local \(Q\)-superlinear (or quadratic) convergence of the algorithm are established. Moreover, calculation of a generalized Jacobian is discussed and numerical results are presented. Cited in 35 Documents MSC: 90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) 65K10 Numerical optimization and variational techniques Keywords:generalized complementarity problem; nonlinear complementarity problem; semi-smooth equation; trust region method; global and superlinear convergence Software:PATH Solver PDFBibTeX XMLCite \textit{H. Jiang} et al., SIAM J. Optim. 8, No. 1, 140--157 (1998; Zbl 0911.90324) Full Text: DOI