A Superlinearly Convergent Algorithm for the Monotone Nonlinear Complementarity Problem Without Uniqueness and Nondegeneracy Conditions

References

  • Bertsekas D. P.Nonlinear Programming (1995) (Athena Scientific, Belmont, MA) Google Scholar
  • Chen X. Smoothing methods for complementarity problems and their applications: A survey. J. Oper. Res. Soc. Japan (2000) 43:32–47CrossrefGoogle Scholar
  • Dan H., Yamashita N., Fukushima M. Convergence properties of the inexact Levenberg-Marquardt method under local error bound conditions. Optimization Methods and Software (2001) . ForthcomingGoogle Scholar
  • De Luca T., Facchinei F., Kanzow C. A semismooth equation approach to the solution of nonlinear complementarity problems. Math. Programming (1996) 75:407–439CrossrefGoogle Scholar
  • Facchinei F., Kanzow C. A nonsmooth inexact Newton method for the solution of large-scale nonlinear complementarity problems. Math. Programming (1997) 76:493–512CrossrefGoogle Scholar
  • Facchinei F., Kanzow C. Beyond monotonicity in regularization methods for complementarity problems. SIAM J. Control Optim. (1999) 37:1150–1161CrossrefGoogle Scholar
  • Facchinei F., Fischer A., Kanzow C. On the identification of zero variables in an interior-point framework. SIAM J. Optim. (2000) 10:1058–1078CrossrefGoogle Scholar
  • Ferris M. C., Pang J-S. Engineering and economic applications of complementarity problem. SIAM Rev. (1997) 39:669–713CrossrefGoogle Scholar
  • Fischer A. A special Newton-type optimization method. Optimization (1992) 24:269–284CrossrefGoogle Scholar
  • Fischer A. Modified Wilson method for nonlinear programs with nonunique multipliers. Math. Oper. Res. (1999) 24:699–727LinkGoogle Scholar
  • Fletcher R.Practical Methods of Optimization (1987) (John Wiley & Sons, New York) Google Scholar
  • Ortega J. M., Rheinboldt W. C.Iterative Solution of Nonlinear Equations in Several Variables (1970) (Academic Press, New York) Google Scholar
  • Pang J-S. A posteriori error bounds for the linearly-constrained variational inequality problem. Math. Oper. Res. (1987) 12:474–484LinkGoogle Scholar
  • Robinson S. M. Some continuity properties of polyhedral multifunctions. Math. Programming Stud. (1981) 14:206–214CrossrefGoogle Scholar
  • Tseng P. Growth behavior of a class of merit functions for the nonlinear complementarity problem. J. Optim. Theory and Appl. (1996) 89:17–37CrossrefGoogle Scholar
  • Wright S. J. Constraint identification and algorithm stabilization for degenerate nonlinear programs. (2000) . Preprint ANL/MCS-P865-1200, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, ILGoogle Scholar
  • Yamashita N., Fukushima M. The proximal point algorithm with genuine superlinear convergence for the monotone complementarity problem. SIAM J. Optim. (2001) 11:364–379CrossrefGoogle Scholar
  • Yamashita N., Dan H., Fukushima M. On the identification of degenerate indices in the nonlinear complementarity problem with the proximal point algorithm. (2001) . Technical Report 2001-003, Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto, JapanGoogle Scholar
INFORMS site uses cookies to store information on your computer. Some are essential to make our site work; Others help us improve the user experience. By using this site, you consent to the placement of these cookies. Please read our Privacy Statement to learn more.