Mathematical programs with complementarity constraints: Convergence properties of a smoothing method

Mathematics of Operations Research

Volumn 32, Issue 2, 2007, Pages 467-483

  Bouza, Gemayqzel ^a   Still, Georg ^b  

^a UNIVERSITY OF HAVANA   (Cuba)

^b UNIVERSITY OF TWENTE   (Netherlands)

Author keywords

Genericity; Mathematical programs with complementarity constraints; Rate of convergence; Smoothing method

Indexed keywords

CONSTRAINT THEORY; CONVERGENCE OF NUMERICAL METHODS; PROBLEM SOLVING;

RATE OF CONVERGENCE; SMOOTHING METHODS;

MATHEMATICAL PROGRAMMING;

EID: 38549103207     PISSN: 0364765X     EISSN: 15265471     Source Type: Journal    
DOI: 10.1287/moor.1060.0245     Document Type: Article

References (19)

1. Chen, C., O. L. Mangasarian. 1995. Smoothing methods for convex inequalities and linear complementarity problems. Math. Programming 71 51-69.
2. Chen, Y., M. Florian. 1995. The nonlinear bilevel programming problem: Formulations, regularity and optimality conditions. Optimization 32 193-209.
3. Facchinei, F., H. Jiang, L. Qi. 1999. A smoothing method for mathematical programs with equilibrium problems. Math. Programming 95 107-134.
4. Fukushima, M., G.-H. Lin. 2005. A modified relaxation scheme for mathematical programs with complementary constraints. Ann. Oper. Res. 133 63-84.
5. Fukushima, M., J.-S. Pang. 1999. Convergence of a smoothing continuation method for mathematical programs with complementarity constraints. M. Thera, R. Tichatschke, eds. Ill-Posed Variational Problems and Regularization Techniques, Lecture Notes in Econom. Math. Systems, Vol. 477. Springer-Verlag, Berlin/Heidelberg, Germany, 99-110.
6. Guddat, J., F. Guerra, H. Th. Jongen. 1990. Parametric Optimization: Singularities, Pathfollowing and Jumps. Teubner and John Wiley, Chichester, UK.
7. Hu, X. 2004. On the convergence of general regularization and smoothing schemes for mathematical programs with complementarity constraints. Optimization 53 39-50.
8. Hu, X., D. Ralph. 2002. A note on sensitivity of value functions of mathematical programs with complementarity constraints. Math. Programming, Ser. A 93 265-279.
9. Leyffer, S. 2003. Mathematical programs with complementarity constraints. Working paper, ANA/MCSP1026-0203, Argonne National Lab., Argonne, IL.
10. Lin, G. H., M. Fukushima. 2003. New relaxation method for mathematical programs with complementarity constraints. J. Optim. Theory Appl. 118(1) 81-116.
11. Luo, Z. Q., J. S. Pang, D. Ralph. 1996. Mathematical Programs with Equilibrium Constraints. Cambridge University Press, Cambridge, UK.
12. Outrata, J., M. Kocvara, J. Zowe. 1998. Nonsmooth Approach to Optimization Problems with Equilibrium Constraints: Theory, Applications and Numerical Results. Nonconvex Optimization and Its Applications, Vol. 28. Kluwer Academic Publishers, Dordrecht, The Netherlands.
13. Ralph, D., S. J. Wright. 2004. Some properties of regularization and penalization schemes for MPECS. Optim. Methods Software 19 527-556.
14. Scheel, H., S. Scholtes. 2000. Mathematical programs with complementarity constraints: Stationarity, optimality and sensitivity. Math. Oper. Res. 25(1) 1-21.
15. Scholtes, S. 2001. Convergence properties of a regularization scheme for mathematical programs with complementarity constraints. SIAM J. Optim. 11(4) 918-936.
16. Scholtes, S., M. Stöhr. 2001. How stringent is the linear independence assumption for mathematical programs with stationary constraints? Math. Oper. Res. 26(4) 851-863.
17. Stein, O., G. Still. 2003. Solving semi-infinite optimization problems with interior point techniques. SIAM J. Control Optim. 42(3) 769-788.
18. Still, G., M. Streng. 1996. Survey paper: Optimality conditions in smooth nonlinear optimization. J. Optim. Appl. Theory 90(3) 483-516.
19. Wright, S. J., D. Orban. 2002. Properties of the log-barrier function on degenerate nonlinear programs. Math. Oper. Res. 27(3) 585-613.