Unconstrained optimization reformulation of the generalized nonlinear complementarity problem and related method

Optimization

Volumn 54, Issue 6, 2005, Pages 563-577

  Wang, Yi Ju ^a,b   Zhang, Xin Zhen ^a   Qi, Li Qun ^b  

^a QUFU NORMAL UNIVERSITY   (China)

^b HONG KONG POLYTECHNIC UNIVERSITY   (Hong Kong)

Author keywords

GNCP; Optimization reformulation; Quadratical convergence

Indexed keywords

EID: 30944443390     PISSN: 02331934     EISSN: None     Source Type: Journal    
DOI: 10.1080/02331930500342625     Document Type: Article

References (14)

1. Andreani, R., Friedlander, A. and Santos, S.A., 2001, On the resolution of the generalized nonlinear complementarity problem. SIAM Journal on Optimization, 12, 303-321.
2. 1 functions and the Maratos effect. Operations Research Letters, 17, 131-137.
3. Facchinei, F., and Pang, J.S., 2003, Finite-Dimensional Variatianal Inequalities and Complementarity Problems (New York, NY: Springer).
4. Ferris, M.C. and Kanzow, C., 2002, Complementarity and related problems. In: P.M. Pardalos and M.G.C. Resende (Eds) Handbook on Applied Optimization (New York, NY: Oxford University Press), pp. 514-530.
5. Fischer, A., 1992, A special Newton-type optimization method. Optimization, 24, 269-284.
6. Fukushima, M., 1996, Merit functions for variational inequality and complementarity problems. In: G. Di Pillo and F. Giannessi (Eds) Nonlinear Optimization and Applications (New York: Plenum Publishing Corporation), pp. 155-170.
7. Jiang, H., Fukushima, M., Qi, L. and Sun, D., 1998, A trust region method for solving generalized complementarity problems. SIAM Journal on Optimization, 8, 140-157.
8. Jiang, H. and Ralph, D., 1999, Global and local superlinear convergence analysis of Newton-type methods for semismooth equations with smooth least squares. Reformulation. In: M. Fukushima and L. Qi (Eds) Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods (Dordrecht: Kluwer Academic Publishers, B.V.), pp. 181-209.
9. Kanzow, C., 1996. Nonlinear Complementarity as Unconstrained Optimization. Journal of Optimization Theory and Applications, 88(1), 139-155.
10. Kanzow, C. and Fukushima, M., 1996, Equivalence of the generalized complementarity problem to differentiable unconstrained minimization. Journal of Optimization Theory and Applications, 90, 581-603.
11. Kanzow, C., Yamashita, N., and Fukushima, M., 1997, New NCP-functions and their properties. Journal of Optimization Theory and Applications, 94, 115-135.
12. Mangasarian, O.L. and Solodov, M.V., 1993, Nonlinear complementarity as unconstrained and constrained minimization. Mathematical Programming, 62, 277-297.
13. Solodov, M.V., 1999, Some optimization reformulations of the extended linear complementarity problem. Computational Optimization and Applications, 13, 187-200.
14. Tseng, P., Yamashita, N. and Fukushima, M., 1996, Equivalence of complementarity problems to differentiable minimization: a unified approach. SIAM Journal on Optimization, 6, 446-460.