Geodesic
Tikhonov regularization for mathematical programs with generalized complementarity constraints
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 4 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In this paper, in order to solve mathematical programs with generalized nonlinear comple-mentarity constraints, we present a new regularization method of Tikhonov type, based on regularizing an optimization problem with equality constraints. The stability and convergence of the regularized solutions are considered. Numerical examples are given for illustration. 
@article{ZVMMF_2015_55_4_a4,
     author = {Buong Nguyen and Thi Thuy Hoa Nguyen},
     title = {Tikhonov regularization for mathematical programs with generalized complementarity constraints},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {574},
     year = {2015},
     volume = {55},
     number = {4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_4_a4/}
}
TY  - JOUR
AU  - Buong Nguyen
AU  - Thi Thuy Hoa Nguyen
TI  - Tikhonov regularization for mathematical programs with generalized complementarity constraints
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2015
SP  - 574
VL  - 55
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_4_a4/
LA  - en
ID  - ZVMMF_2015_55_4_a4
ER  - 
%0 Journal Article
%A Buong Nguyen
%A Thi Thuy Hoa Nguyen
%T Tikhonov regularization for mathematical programs with generalized complementarity constraints
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2015
%P 574
%V 55
%N 4
%U http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_4_a4/
%G en
%F ZVMMF_2015_55_4_a4
Buong Nguyen; Thi Thuy Hoa Nguyen. Tikhonov regularization for mathematical programs with generalized complementarity constraints. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 4. http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_4_a4/

[1] Z. Q. Luo, J. S. D. Pang, D. Ralph, Mathematical Programs with Equilibrium Constraints, Cambridge Univ. Press, Cambridge, UK, 1996 | MR

[2] J. Outrata, M. Kocvara, J. Zowe, Nonsmooth Approach to Optimization Problem with Equilibrium Constraints, Kluwer Academic, Dordrecht, 1998 | MR

[3] M. Ferris, J. Pang, “Engineering and economic applications of complementarity constraints”, SIAM Rev., 39:4 (1997), 669–713 | MR | Zbl

[4] M. Fukushima, Z. Q. Luo, J. S. Pang, “A globally convergent sequential quadratic programming algorithm for mathematical programs with linear complementarity constraints”, Comput. Optim. Appl., 10 (1998), 5–34 | MR | Zbl

[5] H. Jiang, D. Ralph, “Smooth SQP methods for mathematical programs with complementarity constraints”, SIAM J. Optim., 10 (2000), 779–808 | MR | Zbl

[6] M. Monteiro, H. Rodrigues, “Combining the regularization strategy and the SQP to solve MPCC-AMATLAV implementation”, J. Comput. Appl. Math., 235:18 (2011), 5348–5356 | MR | Zbl

[7] R. Fletcher, S. Leyffer, D. Ralph, S. Scholtes, “Local convergence of SQP method for mathematical programs with equilibrium constraints”, SIAM J. Optim., 17:1 (2006), 259–286 | MR | Zbl

[8] X. Chen, M. Fukushima, A smoothing method for mathematical programs with P-matrix linear complementarity constraints, Technical Report 2001-008, Department of Applied Mathematics and Physics, Graduate School on Informatics, Kyoto University, Kyoto, Japan, 2001

[9] X. Hu, D. Ralph, “Convergence of a penalty method for mathematical programs with equilibrium constraints”, J. Optim. Theory Appl., 123:2 (2004), 365–390 | MR

[10] X. X. Huang, X. Q. Yang, D. L. Zhu, A sequential smooth penalty approach to mathematical programs with complementarity constraints, Manuscript, Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong, 2001

[11] Z. Q. Luo, J. S. Pang, D. Ralph, S. Q. Wu, “Exact penalization and stationary conditions of mathematical programs with equilibrium constraints”, Math. Program., 75 (1996), 19–76 | MR | Zbl

[12] S. Scholtes, M. Stohr, “Exact penalization of mathematical programs with complementarity constraints”, SIAM J. Control Optim., 37 (1999), 617–652 | MR | Zbl

[13] M. Monteiro, J. Meira, “A penalty method and a regularization strategy to solve MPCC”, Int. J. Comput. Math., 88:1 (2011), 145–149 | MR | Zbl

[14] M. Pukushima, P. Tseng, “An implementable active-set algorithm for computing a B-stationary point of the mathematical programs with linear complementarity constraints”, SIAM J. Optim., 12 (2002), 724–739 | MR

[15] F. Facchinei, H. Jiang, L. Qi, “A smoothing method for mathematical programs with equilibrium constraints”, Math. Program., 85 (1999), 107–134 | MR | Zbl

[16] M. Pukushima, J. S. Pang, “Convergence of a smoothing continuation method for mathematical programs with complementarity constraints”, Ill-Posed Variational Problems and Regularization Techniques, Lecture Notes in Economics and Mathematica Systems, 447, Springer, Berlin, 1999, 105–116 | MR

[17] G. H. Lin, M. Fukushima, “A modified relaxation scheme for mathematical programs with complementarity constraints”, Ann. Oper. Res., 133:1 (2005), 63–84 | MR | Zbl

[18] S. Scholtes, “Convergence properties of a regularization scheme for mathematical programs with complementarity constraints”, SIAM J. Optim., 11 (2001), 918–936 | MR | Zbl

[19] S. I. Birbil, S. C. Fang, J. Han, “Entropic regularization approach for mathematical programs with equilibrium constraints”, Comput. Oper. Res., 31 (2004), 2249–2262 | MR | Zbl

[20] O. L. Mangasarian, Regularized linear programs equilibrium constraints, Mathematical Programming Technical Report 97-13, November 1997; Reformulation-Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods, eds. M. Rikushima, Liqun Qi, Kluwer Academic, 1998, 259–268 | MR

[21] Ng. Buong, “Tikhonov regularization for a general constrained optimization problems”, Comput. Math. Math. Phys., 47:10 (2007), 1583–1588 | MR

[22] F. P. Vasilev, Numerical Methods for Solving Extremal Problems, Nauka, M., 1980 (in Russian) | MR

[23] O. A. Liskovets, Variational Methods for the Solution of Unstable Problems, Nauka i Tekhnika, Minsk, 1981 (in Russian) | MR

[24] H. H. Bauschke, P. L. Combettes, Convex Analysis and Monotone Operator Theory in Hilbert Spaces, Springer, Berlin, 2010 | MR

[25] A. Vardi, “A trust region algorithm for equality constrained minimization: convergence properties and implementation”, SIAM J. Numer. Anal., 4 (1985), 575–591 | MR

[26] Y. Yuan, “A class of globally convergent conjugate gradient methods”, Sci. China, 46 (2003), 253–261 | MR