Properties of restricted NCP functions for nonlinear complementarity problems

Journal of Optimization Theory and Applications

Volumn 98, Issue 3, 1998, Pages 701-717

  Yamashita, N ^a  

^a KYOTO UNIVERSITY   (Japan)

Author keywords

Bounded level sets; Constrained optimization reformulations; Merit functions; Nonlinear complementarity problems; Restricted NCP functions

Indexed keywords

EQUIVALENCE CLASSES; FUNCTIONS;

BOUNDED LEVEL SET; CONSTRAINED OPTIMIZATION REFORMULATION; LEVEL SET; MERIT FUNCTION; MINIMIZATION PROBLEMS; NCP FUNCTION; NONLINEAR COMPLEMENTARITY PROBLEM; OPTIMIZATION REFORMULATION; PROPERTY; RESTRICTED NCP FUNCTION;

CONSTRAINED OPTIMIZATION;

EID: 0039489819     PISSN: 00223239     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1022684215427     Document Type: Article

References (17)

1. FERRIS, M. C., and PANG, J. S., Complementarity and Variational Problems: State of the Art, SIAM, Philadelphia, Pennsylvania, 1997.
2. FISCHER, A., An NCP Function and Its Use for the Solution of Complementarity Problems, Recent Advances in Nonsmooth Optimization, Edited by D. Z. Du, L. Qi, and R. S. Womersley, World Scientific Publishers, Singapore, pp. 88-105, 1995.
3. FUKUSHIMA, M., Merit Functions for Variational Inequality and Complementarity Problems, Nonlinear Optimization and Applications, Edited by G. Di Pillo and F. Giannessi, Plenum Press, New York, New York, pp. 155-170, 1996.
4. GEIGER, C., and KANZOW, C., On the Resolution of Monotone Complementarity Problems, Computational Optimization and Applications, Vol. 5, pp. 155-173, 1996.
5. KANZOW, C., Nonlinear Complementarity as Unconstrained Optimization, Journal of Optimization Theory and Applications, Vol. 88, pp. 139-155, 1996.
6. KANZOW, C., YAMASHITA, N., and FUKUSHIMA, M., New NCP Functions and Their Properties, Journal of Optimization Theory and Applications, Vol. 92, pp. 115-135, 1997.
7. LUO, Z. Q., and TSENG, P., A New Class of Merit Functions for the Nonlinear Complementarity Problem, Complementarity and Variational Problems: State of the Art, Edited by M. C. Ferris and J. S. Pang, SIAM, Philadelphia, Pennsylvania, pp. 204-225, 1997.
8. MANGASARIAN, O. L., and SOLODOV, M. V., Nonlinear Complementarity as Unconstrained and Constrained Minimization, Mathematical Programming, Vol. 62, pp. 277-297, 1993.
9. MOŔE, J. J., Global Methods for Nonlinear Complementarity Problems, Mathematics of Operations Research, Vol. 21, pp. 589-614, 1996.
10. YAMASHITA, N., and FUKUSHIMA, M., On Stationary Points of the Implicit Lagrangian for Nonlinear Complementarity Problems, Journal of Optimization Theory and Applications, Vol. 84, pp. 653-663, 1995.
11. FACCHINEI, F., and KANZOW, C., On Unconstrained and Constrained Stationary Points of the Implicit Lagrangian, Journal of Optimization Theory and Applications, Vol. 92, pp. 99-115, 1997.
12. FISCHER, A., A New Constrained Optimization Reformulation for Complementarity Problems, Preprint MATH-NM-10-1995, Institute for Numerical Mathematics, Technical University of Dresden, Dresden, Germany, 1995.
13. LESCRENIER, M., Convergence of Trust-Region Algorithms for Optimization with Bounds When Strict Complementarity Does Not Hold, SIAM Journal on Numerical Analysis, Vol. 28, pp. 476-495, 1991.
14. SOLODOV, M. V., On Stationary Points of Bound-Constrained Minimization Reformulations of Complementarity Problems, Journal of Optimization Theory and Applications, Vol. 94, pp. 449-467, 1997.
15. FUKUSHIMA, M., Equivalent Differentiate Optimization Problems and Descent Methods for Asymmetric Variational Inequality Problems, Mathematical Programming, Vol. 53, pp. 99-110, 1992.
16. DE LUCA, T., FACCHINEI, F., and KANZOW, C., A Semismooth Equation Approach to the Solution of Nonlinear Complementarity Problems, Mathematical Programming, Vol. 75, pp. 407-439, 1996.
17. TSENG, P., Growth Behavior of a Class of Merit Functions for the Nonlinear Complementarity Problem, Journal of Optimization Theory and Applications, Vol. 89, pp. 17-37, 1996.