Citation: |
[1] |
S. I. Birbil, G. Gürkan and O. Listes, Solving stochastic mathematical programs with complementarity constraints using simulation, Math. Oper. Res., 31 (2006), 739-760.doi: 10.1287/moor.1060.0215. |
[2] |
R. W. Cottle and G. B. Dantzig, A generalization of the linear complementarity problem, J. Combinatorial Theory, 8 (1970), 79-90.doi: 10.1016/S0021-9800(70)80010-2. |
[3] |
F. H. Clarke, "Optimization and Nonsmooth Analysis," John Wiley and Sons, New York, 1983. |
[4] |
M. Fukushima and J. S. Pang, Convergence of a smoothing continuation method for mathematical programs with complementarity constraints, in "Ill-Posed Variational Problems and Regularization Techniques" (eds. M. Thera and R. Tichatschke), Springer-Verlag, Berlin/Heidelberg, (1999), 99-110.doi: 10.1007/978-3-642-45780-7_7. |
[5] |
A. Fischer, A special Newton-type optimization method, Optimization, 24 (1992), 269-284.doi: 10.1080/02331939208843795. |
[6] |
M. S. Gowda and R. Sznajder, A generalization of the Nash equilibrium theorem on bimatrix games, International Journal of Game Theory, 25 (1996), 1-12.doi: 10.1007/BF01254380. |
[7] |
Z. Huang and J. Sun, A smoothing Newton algorithm for mathematical programs with complementarity constraints, Journal of Industrial and Management Optimization, 1 (2005), 153-170.doi: 10.3934/jimo.2005.1.153. |
[8] |
X. Liu and J. Sun, Generalized stationary points and an interior point method for mathematical programs with equilibrium constraints, Mathematical Programming, 101 (2004), 231-261.doi: 10.1007/s10107-004-0543-6. |
[9] |
X. Liu, G. Perakis and J. Sun, A robust SQP method for mathematical programs with linear complementarity constraints, Computational Optimization and Applications, 34 (2006), 5-33.doi: 10.1007/s10589-005-3075-y. |
[10] |
Z. Q. Luo, J. S. Pang and D. Ralph, "Mathematical Programs with Equilibrium Constraints," Cambridge University Press, Cambridge, UK, 1996.doi: 10.1017/CBO9780511983658. |
[11] |
M. Kočvara and J. V. Outrata, Optimization problems with equilibrium constraints and their numerical solution, Math. Program., 101 (2004), 119-149.doi: 10.1007/s10107-004-0539-2. |
[12] |
J. Peng and Z. Lin, A non-interior continuation method for generalized linear complementarity problems, Mathematical Programming, 86 (1999), 533-563.doi: 10.1007/s101070050104. |
[13] |
H. Qi and L. Liao, A smoothing Newton method for extended vertical linear complementarity problems, SIAM Joural of Matrix Analysis and Applications, 21 (1999), 45-66.doi: 10.1137/S0895479897329837. |
[14] |
R. T. Rockafellar and R. J. B. Wets, "Variational Analysis," Berlin Heidelberg, 1998.doi: 10.1007/978-3-642-02431-3. |
[15] |
R. T. Rockafellar, "Convex Analysis," Princeton University Press, Princeton, New Jersey, 1970. |
[16] |
H. Scheel and S. Scholtes, Mathematical programs with complementarity constraints: Stability, optimality, and sensitivity, Math. Oper. Res., 25 (2000), 1-22.doi: 10.1287/moor.25.1.1.15213. |
[17] |
H. V. Stackelberg, "The Theory of Market Economy," Oxford University Press, London, 1952. |
[18] |
H. Yin and J. Zhang, Global convergence of a smooth approximation method for mathematical programs with complementarity constraints, Math. Meth. Oper. Res., 64 (2006), 255-269.doi: 10.1007/s00186-006-0076-2. |
[19] |
N. D. Yen, Stability of the solution set of perturbed nonsmooth inequality systems and application, Journal of Optimization Theory and Applications, 93 (1997), 199-225.doi: 10.1023/A:1022662120550. |
[20] |
J. Zhang, L. Zhang and S. Lin, A class of smoothing SAA methods for a stochastic mathematical program with complementarity constraints, J. Math. Anal. Appl., 387 (2012), 201-220.doi: 10.1016/j.jmaa.2011.08.073. |
[21] |
J. Zhang, L. Zhang and W. Wang, On constraint qualifications in terms of approximate Jacobians for nonsmooth continuous optimization problems, Nonlinear Analysis, 75 (2012), 2566-2580.doi: 10.1016/j.na.2011.11.003. |