On the convergence of general regularization and smoothing schemes for mathematical programs with complementarity constraints

Optimization

Volumn 53, Issue 1, 2004, Pages 39-50

  Hu, Xinmin ^a  

^a CSIRO   (Australia)

Author keywords

Complementarity constraints; Linear independence constraint qualification; Nonlinear programming; Stationary points

Indexed keywords

EID: 1642392482     PISSN: 02331934     EISSN: None     Source Type: Journal    
DOI: 10.1080/02331930410001661208     Document Type: Article

References (16)

1. J.F. Bard (1998). Practical Bilevel Optimization: Algorithms and Applications. Kluwer Academic Publishers, Dordrecht.
2. Y. Chen and M. Florian (1995). The nonlinear bilevel programming problem: formulations, regularity and optimality conditions. Optimization, 32, 193-209.
3. F. Facchinei, H. Jiang and L. Qi (1999). A smoothing method for mathematical programs with equilibrium constraints. Mathematical Programming, 85, 107-134.
4. A. Fischer (1992). A special Newton-type optimization method. Optimization, 24, 269-284.
5. M. Fukushima and J.-S. Pang (2000). Convergence of a smoothing continuation method for mathematical programs with complementarity constraints. In: M. Théra and R. Tichatschke (Eds.), Ill-posed Variational Problems and Regularization Techniques, pp. 99-110. Springer, Berlin, Heidelberg.
6. X. Hu and D. Ralph (2003). Convergence of a penalty method for mathematical programming with complementarity constraints. Journal of Optimization Theory and Applications (to appear).
7. X.X. Huang, X.Q. Yang and D.L. Zhu (2001). A sequential smooth penalization approach to mathematical programs with complementarity constraints, manuscript. Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong, China.
8. H. Jiang and D. Ralph (2000). Smooth SQP methods for mathematical programs with nonlinear complementarity constraints. SIAM Journal on Optimization, 10, 779-808.
9. C. Kanzow (1996). Some noninterior continuation methods for linear complementarity problems. SIAM Journal on Matrix Analysis and Applications, 17, 851-868.
10. M. Kojima (1980). Strongly stable stationary solutions in nonlinear programming. In: S. Robinson (Ed.), Analysis and Computation of Fixed Points, pp. 93-138. Academic Press, New York.
11. Z.-Q. Luo, J.-S. Pang and D. Ralph (1996). Mathematical Programs with Equilibrium Constraints., Cambridge University Press, Cambridge.
12. J.V. Outrata, M. Kocvara and J. Zowe (1998). Nonsmooth Approach to Optimization Problems with Equilibrium Constraints: Theory, Applications and Numerical Results. Kluwer Academic Publishers, Dordrecht.
13. H. Scheel and S. Scholtes (2000). Mathematical programs with complementarity constraints: stationarity, optimality, and sensitivity. Mathematics of Operations Research, 25, 1-22.
14. S. Scholtes (2001). Convergence properties of a regularization scheme for mathematical programs with complementarity constraints. SIAM J. Optim., 11, 918-936.
15. S. Scholtes (2001). Private communications.
16. S. Scholtes (2003). Private communications.