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Optimal control of electrorheological clutch described by nonlinear parabolic equation with nonlocal boundary conditions
Sample average approximation method for stochastic complementarity problems with applications to supply chain supernetworks
1. | School of Management Science and Engineering, Dalian University of Technology, Dalian 116023, China |
2. | School of Computational and Applied Mathematics, University of the Witwatersrand, Private Bag-3, Wits-2050, Johannesburg, South Africa |
3. | School of Mathematical Science, Dalian University of Technology, Dalian 116024, China |
References:
[1] |
F. Bastin, C. Cirllo and P. L. Toint, Convergence theory for nonconvex stochastic programming with an application to mixed logit,, Mathematical Programming, 108 (2006), 207.
doi: 10.1007/s10107-006-0708-6. |
[2] |
X. Chen and M. Fukushima, Expected residual minimization method for stochastic linear complementarity problems,, Mathematics of Operations Research, 30 (2005), 1022.
doi: 10.1287/moor.1050.0160. |
[3] |
X. Chen, C. Zhang and M. Fukushima, Robust solution of stochastic matrix linear complementarity problems,, Mathematical Programming, 117 (2009), 51.
|
[4] |
F. H. Clarke, "Optimization and Nonsmooth Analysis,", SIAM, (1990).
|
[5] |
R. W. Cottle, J.-S. Pang and R. Stone, "The linear Complementary Problems,", Academic Press, (1992).
|
[6] |
J. Dong, D. Zhang and A. Nagurney, A supply chain network equilibrium model with random demands,, European Journal of Operational Research, 156 (2004), 194.
doi: 10.1016/S0377-2217(03)00023-7. |
[7] |
F. Facchinei and J-S. Pang, "Finite-Dimensional Variational Inequalities and Complementarity Problems,", Springer, (2003).
|
[8] |
H. Fang, X. Chen and M. Fukushima, Stochastic $R_0$ Matrix linear complementarity problems,, SIAM Journal on Optimization, 18 (2007), 482.
doi: 10.1137/050630805. |
[9] |
G. Gürkan, A. Y. Özge and S. M. Robinson, Sample-path solutions of stochastic variational inequalities,, Mathematical Programming, 84 (1999), 313.
doi: 10.1007/s101070050024. |
[10] |
G. H. Lin, X. Chen and M. Fukushima, New restricted NCP functions and their applications to stochastic NCP and stochastic MPEC,, Optimization, 56 (2007), 641.
doi: 10.1080/02331930701617320. |
[11] |
G. H. Lin and M. Fukushima, New reformulations for stochastic nonlinear complementarity problems,, Optimization Methods and Software, 21 (2006), 551.
doi: 10.1080/10556780600627610. |
[12] |
F. W. Meng and H. Xu, A regularized sample average approximation method for stochastic mathematical programs with nonsmooth equality constraints,, SIAM Journal on Optimization, 17 (2006), 891.
doi: 10.1137/050638242. |
[13] |
A. Nagurney, "Network Economics: a Variational Inequality Approach,", Kluwer Academic Publishers, (1999). Google Scholar |
[14] |
A. Nagurney, J. Cruz, J. Dong and D. Zhang, Supply chain networks, electronic commence, and supply side and demand side risk,, European Journal of Operational Research, 164 (2005), 120.
doi: 10.1016/j.ejor.2003.11.007. |
[15] |
A. Nagurney and J. Dong, "Super-Networks: Decision-Making for the Information Age,", Edward Elgar Publishers, (2002). Google Scholar |
[16] |
S. M. Robinson, Analysis of sample-path optimization,, Mathematics of Operations Research, 21 (1996), 513.
doi: 10.1287/moor.21.3.513. |
[17] |
A. Ruszcynski and A. Shapiro, Eds., "Stochastic Programming,", Handbooks in OR$&$MS, (2003).
|
[18] |
T. Santoso, S. Ahmed and A. Shapiro, A stochastic programming approach for suppy chain network design under uncertainty,, European Journal of Operational Research, 167 (2005), 96.
doi: 10.1016/j.ejor.2004.01.046. |
[19] |
A. Shapiro, Stochastic mathematical programs with equilibrium constraints,, Journal of Optimization Theory and Application, 128 (2006), 223.
doi: 10.1007/s10957-005-7566-x. |
[20] |
A. Shapiro and H. Xu, Stochastic mathematical programs with equilibrium constraints, modeling and sample average approximation,, Optimization, 57 (2008), 395.
doi: 10.1080/02331930801954177. |
[21] |
R. Storn and K. Price, Differential evolution - a simple and efficient heuristic for global optimization over continuous spaces,, Journal of Global Optimization, 11 (1997), 341.
doi: 10.1023/A:1008202821328. |
[22] |
H. Xu and F. Meng, Convergence analysis of sample average approximation methods for a class of stochastic mathematical programs with equality constraints,, Mathematics of Operations Research, 32 (2007), 648.
doi: 10.1287/moor.1070.0260. |
[23] |
C. Zhang and X. Chen, Stochastic nonlinear complementary problem and application to traffic equilibrium under uncertainty,, Journal of Optimization Theory and Applications, 137 (2008), 277.
doi: 10.1007/s10957-008-9358-6. |
show all references
References:
[1] |
F. Bastin, C. Cirllo and P. L. Toint, Convergence theory for nonconvex stochastic programming with an application to mixed logit,, Mathematical Programming, 108 (2006), 207.
doi: 10.1007/s10107-006-0708-6. |
[2] |
X. Chen and M. Fukushima, Expected residual minimization method for stochastic linear complementarity problems,, Mathematics of Operations Research, 30 (2005), 1022.
doi: 10.1287/moor.1050.0160. |
[3] |
X. Chen, C. Zhang and M. Fukushima, Robust solution of stochastic matrix linear complementarity problems,, Mathematical Programming, 117 (2009), 51.
|
[4] |
F. H. Clarke, "Optimization and Nonsmooth Analysis,", SIAM, (1990).
|
[5] |
R. W. Cottle, J.-S. Pang and R. Stone, "The linear Complementary Problems,", Academic Press, (1992).
|
[6] |
J. Dong, D. Zhang and A. Nagurney, A supply chain network equilibrium model with random demands,, European Journal of Operational Research, 156 (2004), 194.
doi: 10.1016/S0377-2217(03)00023-7. |
[7] |
F. Facchinei and J-S. Pang, "Finite-Dimensional Variational Inequalities and Complementarity Problems,", Springer, (2003).
|
[8] |
H. Fang, X. Chen and M. Fukushima, Stochastic $R_0$ Matrix linear complementarity problems,, SIAM Journal on Optimization, 18 (2007), 482.
doi: 10.1137/050630805. |
[9] |
G. Gürkan, A. Y. Özge and S. M. Robinson, Sample-path solutions of stochastic variational inequalities,, Mathematical Programming, 84 (1999), 313.
doi: 10.1007/s101070050024. |
[10] |
G. H. Lin, X. Chen and M. Fukushima, New restricted NCP functions and their applications to stochastic NCP and stochastic MPEC,, Optimization, 56 (2007), 641.
doi: 10.1080/02331930701617320. |
[11] |
G. H. Lin and M. Fukushima, New reformulations for stochastic nonlinear complementarity problems,, Optimization Methods and Software, 21 (2006), 551.
doi: 10.1080/10556780600627610. |
[12] |
F. W. Meng and H. Xu, A regularized sample average approximation method for stochastic mathematical programs with nonsmooth equality constraints,, SIAM Journal on Optimization, 17 (2006), 891.
doi: 10.1137/050638242. |
[13] |
A. Nagurney, "Network Economics: a Variational Inequality Approach,", Kluwer Academic Publishers, (1999). Google Scholar |
[14] |
A. Nagurney, J. Cruz, J. Dong and D. Zhang, Supply chain networks, electronic commence, and supply side and demand side risk,, European Journal of Operational Research, 164 (2005), 120.
doi: 10.1016/j.ejor.2003.11.007. |
[15] |
A. Nagurney and J. Dong, "Super-Networks: Decision-Making for the Information Age,", Edward Elgar Publishers, (2002). Google Scholar |
[16] |
S. M. Robinson, Analysis of sample-path optimization,, Mathematics of Operations Research, 21 (1996), 513.
doi: 10.1287/moor.21.3.513. |
[17] |
A. Ruszcynski and A. Shapiro, Eds., "Stochastic Programming,", Handbooks in OR$&$MS, (2003).
|
[18] |
T. Santoso, S. Ahmed and A. Shapiro, A stochastic programming approach for suppy chain network design under uncertainty,, European Journal of Operational Research, 167 (2005), 96.
doi: 10.1016/j.ejor.2004.01.046. |
[19] |
A. Shapiro, Stochastic mathematical programs with equilibrium constraints,, Journal of Optimization Theory and Application, 128 (2006), 223.
doi: 10.1007/s10957-005-7566-x. |
[20] |
A. Shapiro and H. Xu, Stochastic mathematical programs with equilibrium constraints, modeling and sample average approximation,, Optimization, 57 (2008), 395.
doi: 10.1080/02331930801954177. |
[21] |
R. Storn and K. Price, Differential evolution - a simple and efficient heuristic for global optimization over continuous spaces,, Journal of Global Optimization, 11 (1997), 341.
doi: 10.1023/A:1008202821328. |
[22] |
H. Xu and F. Meng, Convergence analysis of sample average approximation methods for a class of stochastic mathematical programs with equality constraints,, Mathematics of Operations Research, 32 (2007), 648.
doi: 10.1287/moor.1070.0260. |
[23] |
C. Zhang and X. Chen, Stochastic nonlinear complementary problem and application to traffic equilibrium under uncertainty,, Journal of Optimization Theory and Applications, 137 (2008), 277.
doi: 10.1007/s10957-008-9358-6. |
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