On some NCP-functions based on the generalized Fischer-burmeister function

Asia-Pacific Journal of Operational Research

Volumn 24, Issue 3, 2007, Pages 401-420

  Chen, Jein Shan ^a  

^a NATIONAL TAIWAN NORMAL UNIVERSITY   (Taiwan)

Author keywords

Bounded level sets; Complementarity; Merit function; NCP function; Stationary point

Indexed keywords

FUNCTION EVALUATION; NONLINEAR SYSTEMS; OPTIMIZATION; PROBLEM SOLVING;

BOUNDED LEVEL SETS; COMPLEMENTARITY; FISCHER-BURMEISTER FUNCTION; MERIT FUNCTIONS; STATIONARY POINTS;

FUNCTIONS;

EID: 34547153780     PISSN: 02175959     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0217595907001292     Document Type: Article

References (27)

1. Chen, B, X Chen and C Kanzow (2000). A penalized Fischer-Burmeister NCP-function: theoretical investigation and numerical results. Mathematical Programming, 88, 211-216.
2. Chen, B and PT Harker (1997). Smooth approximations to nonlinear complementarity problems. SIAM Journal on Optimization, 2, 403-420.
3. Chen, J-S and S Pan (2006). A family of NCP-function and a descent method for the nonlinear complementarity problem. To appear in Computational Optimization and Applications.
4. Chen, J-S (2006). The semismooth-related properties of a merit function and a descent method for the nonlinear complementarity problem. Journal of Global Optimization, 36, 565-580.
5. Clarke, FH (1983). Optimization and Nonsmooth Analysis. New York: Wiley.
6. De Luca, T, F Facchinei and C Kanzow (1996). A semismooth equation approximation to the solution of the nonlinear complementarity problems. Mathematical Programming, 75, 407-439.
7. Facchinei, F and J-S Pang (2003). Finite-Dimensional Variational Inequalities and Complementarity Problems, Vols. I and II. New York: Springer-Verlag.
8. Facchinei, F and J Soares (1997). A new merit function for nonlinear complementarity problems and a related algorithm. SIAM Journal on Optimization, 7, 225-247.
9. Ferris, MC and J-S Pang (1997). Engineering and economic applications of complementarity problems. SIAM Review, 39, 669-713.
10. Fischer, A (1992). A special Newton-type optimization methods. Optimization, 24, 269-284.
11. Fischer, A (1997). Solution of the monotone complementarity problem with locally Lipschitzian functions. Mathematical Programming, 76, 513-532.
12. Geiger, C and C Kanzow (1996). On the resolution of monotone complementarity problems. Computational Optimization and Applications, 5, 155-173.
13. Harker, PT and J-S Pang (1990). Finite dimensional variational inequality and nonlinear complementarity problem: A survey of theory, algorithms and applications. Mathematical Programming, 48, 161-220.
14. Kanzow, C (1996). Nonlinear complementarity as unconstrained optimization. Journal of Optimization Theory and Applications, 88, 139-155.
15. Kanzow, C and H Kleinmichel (1998). A new class of semismooth Newton-type methods for the nonlinear complementarity problems. Computational Optimizations and Applications, 11, 227-251.
16. Kanzow, C, N Yamashita and M Fukushima (1997). New NCP-functions and their properties. Journal of Optimization Theory and Applications, 94, 115-135.
17. Mangasarian, OL (1976), Equivalence of the complementarity problem to a system of nonlinear equations. SIAM Journal on Applied Mathematics, 31, 89-92.
18. Mifflin, R (1977). Semismooth and semiconvex functions in constrained optimization. SIAM Journal on Control Optimization, 15, 959-972.
19. Pan, S and J-S Chen (2007), A family of penalized NCP functions based on the generalized Fischer-Burmeister functions: Theoretical investigation and numerical results. Submitted.
20. Pang, J-S (1994). Complementarity problems. Handbook of Global Optimization, R Horst and P Pardalos (eds.), pp. 271-338, Boston, MA: Kluwer Academic Publishers.
21. Qi, L-Q (1993). Convergence analysis of some algorithms for solving nonsmooth equations. Mathematics of Operations Research, 18, 227-244.
22. Qi, L-Q (1994). Superlinearly convergent approximate Newton methods for LC optimization problems. Mathematical Programming, 64, 277-294.
23. Qi, L-Q and J Sun (1993). A nonsmooth version of Newton's method. Mathematical Programming, 58, 353-367.
24. Rockafellar, RT and J-B Wets (1998). Variational Analysis, Berlin: Springer-Verlag.
25. Sun, D and L-Q Qi (1999). On NCP-functions. Computational Optimization and Applications, 13, 201-220.
26. Tseng, P (1996), Global behaviour of a class of merit functions for the nonlinear complementarity problem. Journal of Optimization Theory and Applications, 89, 17-37.
27. Yamada, K, N Yamashita and M Fukushima (2000). A new derivative-free descent method for the nonlinear complementarity problems, In: Nonlinear Optimization and Related Topics, GD Pillo and F Giannessi (eds.), Netherlands: Kluwer Academic Publishers, pp. 463-489.