New reformulations for stochastic nonlinear complementarity problems

Optimization Methods and Software

Volumn 21, Issue 4, 2006, Pages 551-564

  Lin, Gui Hua ^a,b   Fukushima, Masao ^b  

^a DALIAN UNIVERSITY OF TECHNOLOGY   (China)

^b KYOTO UNIVERSITY   (Japan)

Author keywords

Convergence; Stationarity; Stochastic mathematical program with equilibrium constraints; Stochastic nonlinear complementarity problem; Subdifferential

Indexed keywords

ALGORITHMS; CONSTRAINT THEORY; MATHEMATICAL MODELS; NONLINEAR EQUATIONS; PROBLEM SOLVING; STOCHASTIC PROGRAMMING;

CONVERGENCE; STATIONARITY; STOCHASTIC MATHEMATICAL PROGRAM WITH EQUILIBRIUM CONSTRAINTS; STOCHASTIC NONLINEAR COMPLEMENTARITY PROBLEM; SUBDIFFERENTIAL;

CONVERGENCE OF NUMERICAL METHODS;

EID: 33745616495     PISSN: 10556788     EISSN: 10294937     Source Type: Journal    
DOI: 10.1080/10556780600627610     Document Type: Conference Paper

References (15)

1. Cottle, R.W., Pang, J.S. and Stone, R.E., 1992, The Linear Complementarity Problem (New York, NY: Academic Press).
2. Gürkan, G., Özge, A.Y. and Robinson, S.M., 1999, Sample-path solution of stochastic variational inequalities. Mathematical Programming, 84, 313-333.
3. Haurie, A. and Moresino, F., 2002, S-adapted oligopoly equilibria and approximations in stochastic variational inequalities. Annals of Operations Research, 114, 183-201.
4. Chen, X. and Fukushima, M., 2005, Expected residual minimization method for stochastic linear complementarity problems. Mathematics of Operations Research, 30, 1022-1038.
5. Luo, Z.Q., Pang, J.S. and Ralph, D., 1996, Mathematical Programs with Equilibrium Constraints (Cambridge, UK: Cambridge University Press).
6. Lin, G.H., Chen, X. and Fukushima, M., 2003, Smoothing implicit programming approaches for stochastic mathematical programs with linear complementarity constraints. Technical Report 2003-2006. Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto, Japan.
7. Lin, G.H. and Fukushima, M., 2005, A class of stochastic mathematical programs with complementarity constraints: reformulations and algorithms. Journal of Industrial and Management Optimization, 1, 99-122.
8. Lin, G.H. and Fukushima, M., 2005, Regularization method for stochastic mathematical programs with complementarity constraints. European Series of Applied and Industrial Mathematics (ESAIM): Control, Optimisation and Calculus of Variations, 11, 252-265.
9. Shapiro, A., 2004, Stochastic mathematical programs with equilibrium constraints. Preprint. School of Industrial and System Engineering, Georgia Institute of Technology, Antalanta, Georgia, USA.
10. Shapiro, A. and Xu, H., 2005, Stochastic mathematical programs with equilibrium constraints, modeling and sample average approximation. Preprint. School of Industrial and System Engineering, Georgia Institute of Technology, Antalanta, Georgia, USA.
11. Xu, H., 2006, An implicit programming approach for a class of stochastic mathematical programs with linear complementarity constraints. SIAM Journal of Optimization, 16, 670-696.
12. Clarke, F.H., 1990, Optimization and Nonsmooth Analysis (Philadelphia: SIAM).
13. Lin, G.H. and Fukushima, M., 2005, A modified relaxation scheme for mathematical programs with complementarity constraints. Annals of Operations Research, 133, 63-84.
14. Lin, G.H. and Fukushima, M., 2003, New relaxation method for mathematical programs with complementarity constraints. Journal of Optimization Theory and Applications, 118, 81-116.
15. Scheel, H.S. and Scholtes, S., 2000, Mathematical programs with complementarity constraints: stationarity, optimality, and sensitivity. Mathematics of Operations Research, 25, 1-22.