QPCOMP is an extremely robust algorithm for solving mixed nonlinear complementarity problems that has fast local convergence behavior. Based in part on the NE/SQP method of Pang and Gabriel (1993), this algorithm represents a significant advance in robustness at no cost in efficiency. In particular, the algorithm is shown to solve any solvable Lipschitz continuous, continuously differentiable, pseudo-monotone mixed nonlinear complementarity problem. QPCOMP also extends the NE/SQP method for the nonlinear complementarity problem to the more general mixed nonlinear complementarity problem. Computational results are provided, which demonstrate the effectiveness of the algorithm.

References in zbMATH (referenced in 30 articles , 1 standard article )

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  1. Chen, Xiaojun; Wang, Zhengyu: Computational error bounds for a differential linear variational inequality (2012)
  2. Chen, Jein-Shan; Pan, Shaohua; Lin, Tzu-Ching: A smoothing Newton method based on the generalized Fischer-Burmeister function for MCPs (2010)
  3. Chen, Jein-Shan; Pan, Shaohua; Yang, Ching-Yu: Numerical comparisons of two effective methods for mixed complementarity problems (2010)
  4. Acary, Vincent; Brogliato, Bernard: Numerical methods for nonsmooth dynamical systems. Applications in mechanics and electronics (2008)
  5. Konnov, Igor V.: Combined relaxation methods for generalized monotone variational inequalities (2007)
  6. Allevi, E.; Gnudi, A.; Konnov, I.V.: The proximal point method for nonmonotone variational inequalities (2006)
  7. Konnov, Igor V.: Application of the proximal point method to a system of extended primal-dual equilibrium problems (2006)
  8. Konnov, I.V.: Application of the proximal point method to nonmonotone equilibrium problems (2003)
  9. Li, Wu; de Nijs, J.J.: An implementation of the QSPLINE method for solving convex quadratic programming problems with simple bound constraints. (2003)
  10. Billups, Stephen C.: A homotopy-based algorithm for mixed complementarity problems (2002)
  11. Konnov, I.V.; Kum, Sangho; Lee, Gue Myung: On convergence of descent methods for variational inequalities in a Hilbert space (2002)
  12. Kanzow, Christian: Strictly feasible equation-based methods for mixed complementarity problems (2001)
  13. Ulbrich, Michael: Nonmonotone trust-region methods for bound-constrained semismooth equations with applications to nonlinear mixed complementarity problems (2001)
  14. Andreani, R.; Martínez, J.M.; Svaiter, B.F.: On the regularization of mixed complementarity problems (2000)
  15. Billups, Stephen C.: Improving the robustness of descent-based methods for semismooth equations using proximal perturbations (2000)
  16. Ferris, Michael C.; Munson, Todd S.: Complementarity problems in GAMS and the PATH solver (2000)
  17. Ferris, Michael C.; Sinapiromsaran, Krung: Formulating and solving nonlinear programs as mixed complementarity problems (2000)
  18. Solodov, Michael V.; Tseng, Paul: Some methods based on the D-gap function for solving monotone variational inequalities (2000)
  19. Facchinei, Francisco; Kanzow, Christian: Beyond monotonicity in regularization methods for nonlinear complementarity problems (1999)
  20. Ferris, Michael C.; Kanzow, Christian; Munson, Todd S.: Feasible descent algorithms for mixed complementarity problems (1999)

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