
Previous Article
Optimal control of electrorheological clutch described by nonlinear parabolic equation with nonlocal boundary conditions
 JIMO Home
 This Issue

Next Article
Existence of anonymous link tolls for decentralizing an oligopolistic game and the efficiency analysis
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 Bag3, Wits2050, 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/s1010700607086. 
[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/S03772217(03)000237. 
[7] 
F. Facchinei and JS. Pang, "FiniteDimensional 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, Samplepath 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). 
[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, "SuperNetworks: DecisionMaking for the Information Age,", Edward Elgar Publishers, (2002). 
[16] 
S. M. Robinson, Analysis of samplepath 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/s109570057566x. 
[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/s1095700893586. 
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/s1010700607086. 
[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/S03772217(03)000237. 
[7] 
F. Facchinei and JS. Pang, "FiniteDimensional 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, Samplepath 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). 
[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, "SuperNetworks: DecisionMaking for the Information Age,", Edward Elgar Publishers, (2002). 
[16] 
S. M. Robinson, Analysis of samplepath 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/s109570057566x. 
[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/s1095700893586. 
[1] 
René Henrion, Christian Küchler, Werner Römisch. Discrepancy distances and scenario reduction in twostage stochastic mixedinteger programming. Journal of Industrial & Management Optimization, 2008, 4 (2) : 363384. doi: 10.3934/jimo.2008.4.363 
[2] 
Zhiping Chen, Youpan Han. Continuity and stability of twostage stochastic programs with quadratic continuous recourse. Numerical Algebra, Control & Optimization, 2015, 5 (2) : 197209. doi: 10.3934/naco.2015.5.197 
[3] 
Suxiang He, Pan Zhang, Xiao Hu, Rong Hu. A sample average approximation method based on a Dgap function for stochastic variational inequality problems. Journal of Industrial & Management Optimization, 2014, 10 (3) : 977987. doi: 10.3934/jimo.2014.10.977 
[4] 
Mei Ju Luo, Yi Zeng Chen. Smoothing and sample average approximation methods for solving stochastic generalized Nash equilibrium problems. Journal of Industrial & Management Optimization, 2016, 12 (1) : 115. doi: 10.3934/jimo.2016.12.1 
[5] 
Rüdiger Schultz. Twostage stochastic programs: Integer variables, dominance relations and PDE constraints. Numerical Algebra, Control & Optimization, 2012, 2 (4) : 713738. doi: 10.3934/naco.2012.2.713 
[6] 
GuiHua Lin, Masao Fukushima. A class of stochastic mathematical programs with complementarity constraints: reformulations and algorithms. Journal of Industrial & Management Optimization, 2005, 1 (1) : 99122. doi: 10.3934/jimo.2005.1.99 
[7] 
Yongchao Liu. Quantitative stability analysis of stochastic mathematical programs with vertical complementarity constraints. Numerical Algebra, Control & Optimization, 2018, 8 (4) : 451460. doi: 10.3934/naco.2018028 
[8] 
Bin Li, Jie Sun, Honglei Xu, Min Zhang. A class of twostage distributionally robust games. Journal of Industrial & Management Optimization, 2018, 13 (5) : 114. doi: 10.3934/jimo.2018048 
[9] 
Chien Hsun Tseng. Applications of a nonlinear optimization solver and twostage comprehensive Denoising techniques for optimum underwater wideband sonar echolocation system. Journal of Industrial & Management Optimization, 2013, 9 (1) : 205225. doi: 10.3934/jimo.2013.9.205 
[10] 
MingYong Lai, ChangShi Liu, XiaoJiao Tong. A twostage hybrid metaheuristic for pickup and delivery vehicle routing problem with time windows. Journal of Industrial & Management Optimization, 2010, 6 (2) : 435451. doi: 10.3934/jimo.2010.6.435 
[11] 
MingZheng Wang, M. Montaz Ali. Penaltybased SAA method of stochastic nonlinear complementarity problems. Journal of Industrial & Management Optimization, 2010, 6 (1) : 241257. doi: 10.3934/jimo.2010.6.241 
[12] 
Jie Zhang, Yue Wu, Liwei Zhang. A class of smoothing SAA methods for a stochastic linear complementarity problem. Numerical Algebra, Control & Optimization, 2012, 2 (1) : 145156. doi: 10.3934/naco.2012.2.145 
[13] 
HuiQiang Ma, NanJing Huang. Neural network smoothing approximation method for stochastic variational inequality problems. Journal of Industrial & Management Optimization, 2015, 11 (2) : 645660. doi: 10.3934/jimo.2015.11.645 
[14] 
Jingzhi Li, Hongyu Liu, Qi Wang. Fast imaging of electromagnetic scatterers by a twostage multilevel sampling method. Discrete & Continuous Dynamical Systems  S, 2015, 8 (3) : 547561. doi: 10.3934/dcdss.2015.8.547 
[15] 
Urszula Foryś, Beata Zduniak. Twostage model of carcinogenic mutations with the influence of delays. Discrete & Continuous Dynamical Systems  B, 2014, 19 (8) : 25012519. doi: 10.3934/dcdsb.2014.19.2501 
[16] 
David J. Aldous. A stochastic complex network model. Electronic Research Announcements, 2003, 9: 152161. 
[17] 
Liping Zhang. A nonlinear complementarity model for supply chain network equilibrium. Journal of Industrial & Management Optimization, 2007, 3 (4) : 727737. doi: 10.3934/jimo.2007.3.727 
[18] 
Yi Zhang, Liwei Zhang, Jia Wu. On the convergence properties of a smoothing approach for mathematical programs with symmetric cone complementarity constraints. Journal of Industrial & Management Optimization, 2018, 14 (3) : 9811005. doi: 10.3934/jimo.2017086 
[19] 
X. X. Huang, D. Li, Xiaoqi Yang. Convergence of optimal values of quadratic penalty problems for mathematical programs with complementarity constraints. Journal of Industrial & Management Optimization, 2006, 2 (3) : 287296. doi: 10.3934/jimo.2006.2.287 
[20] 
G. Buffoni, S. Pasquali, G. Gilioli. A stochastic model for the dynamics of a stage structured population. Discrete & Continuous Dynamical Systems  B, 2004, 4 (3) : 517525. doi: 10.3934/dcdsb.2004.4.517 
2017 Impact Factor: 0.994
Tools
Metrics
Other articles
by authors
[Back to Top]