Unconstrained optimization reformulation for stochastic nonlinear complementarity problems

References

• Gürkan G, Özge AY, Robinson SM. Sample-path solution of stochastic variational inequalities. Math Program. 1999;84:313–333. doi: 10.1007/s101070050024
   Web of Science ®Google Scholar
• Chen X, Fukushima M. Expected residual minimization method for stochastic linear complementarity problems. Math Oper Res. 2005;30:1022–1038. doi: 10.1287/moor.1050.0160
   Web of Science ®Google Scholar
• Zhang C, Chen X. Stochastic nonlinear complementarility problem and applications to traffic equilibrium under uncertainty. J Optim Theory Appl. 2008;137:277–295. doi: 10.1007/s10957-008-9358-6
   Web of Science ®Google Scholar
• Luo MJ, Lin GH. Expected residual minimization method for stochastic variation inequality problems. J Optim Theory Appl. 2009;140:103–116. doi: 10.1007/s10957-008-9439-6
   Web of Science ®Google Scholar
• Ma HQ, Wu M, Huang NJ, et al. Expected residual minimization method for stochastic variational inequality problems with nonlinear perturbations. Appl Math and Comput. 2013;219:6256–6267.
   Web of Science ®Google Scholar
• Lu F, Li SJ. Method of weighted expected residual for solving stochastic variational inequality problems. Appl Math and Comput. 2015;269:651–663.
   Web of Science ®Google Scholar
• Agdeppa RP, Yamashita N, Fukushima M. Convex expected residual models for stochastic affine variational inequality Pproblems and its application to the traffic equilibrium problem. Pac J Optim. 2010;6(1):3–19.
   Web of Science ®Google Scholar
• Lin GH, Fukushima M. New reformulations for stochastic nonlinear complementarity problems. Optim Meth Softw. 2006;21:551–564. doi: 10.1080/10556780600627610
   Web of Science ®Google Scholar
• Fang H, Chen X, Fukushima M. Stochastic R0 matrix linear complementarity problems. SIAM J Optim. 2007;18:482–506. doi: 10.1137/050630805
   Web of Science ®Google Scholar
• Chen X, Zhang C, Fukushima M. Robust solution of monotone stochastic linear complementarity problems. Math Program. 2009;117:51–80. doi: 10.1007/s10107-007-0163-z
   Web of Science ®Google Scholar
• Luo MJ, Lin GH. Convergence results of the ERM method for nonlinear stochastic variation inequality problems. J Optim Theory Appl. 2009;142:569–581. doi: 10.1007/s10957-009-9534-3
   Web of Science ®Google Scholar
• Lu F, Li SJ. Convergence analysis of weighted expected residual method for nonlinear stochastic variation inequality problems. Math Methods Oper Res. 2015;82:229–242. doi: 10.1007/s00186-015-0512-2
   Web of Science ®Google Scholar
• Xie Y, Shanbhag UV. On robust solutions to uncertain linear complementarity problems and their variants. SIAM J Optim. 2016;26(4):2120–2159. doi: 10.1137/15M1010427
   Web of Science ®Google Scholar
• Zhang YF, Chen X. Regularizations for stochastic linear variational inequalities. J Optim Theory Appl. 2014;163:460–481. doi: 10.1007/s10957-013-0514-2
   Web of Science ®Google Scholar
• Yamashita N, Taji K, Fukushima M. Unconstraied optimization reformulations of variational inequality problems. J Optim Theory Appl. 1997;92:439–456. doi: 10.1023/A:1022660704427
   Web of Science ®Google Scholar
• Fukushima M. Equivalent differentiable optimization problems and descent methods for asymmetric variational inequality problems. Math Program. 1992;53:99–110. doi: 10.1007/BF01585696
   Web of Science ®Google Scholar
• Fukushima M. Merit functions for variational inequality and complementarity problems. In: Di Pillo G, Giannessi F, editors. Nonlinear Optimization and Applications. New York (NY): Plenum Press; 1996. p. 155–170.
   Google Scholar
• Facchinei F, Pang JS. Finite-dimensional variational inequalities and complementarity problems. New York (NY): Springer; 2003.
   Google Scholar
• Patrick B. Probability and measure. New York (NY): Wiley; 1995.
   Google Scholar
• Cottle RW, Pang JS, Stone RE. The linear complementarity problem. New York (NY): Academic Press, Inc.; 1992.
   Google Scholar
• Muu LD, Quy NV. DC-gap function and proximal methods for solving Nash-Cournot oligopolistic equilibrium models involving concave cost. J Appl Numer Optim. 2019;1:13–24.
   Google Scholar
• Niederreiter H. Random number generation and Quasi-Monte Carlo methods. Philadelphia (PA): SIAM; 1992.
   Google Scholar
• Birge JR. Quasi-Monte Carlo approaches to option pricing. Ann Arbor: Department of Industrial and Operations Engineering, University of Michigan; 1994. (Technical Report 94-19).
   Google Scholar
• Wordrop JG. Some theoretical aspects of road traffic research. Proc ICE. 1952;1(Part II):325–378.
   Google Scholar
• Li J, Tammer C. Set optimization problems on ordered sets. Appl Set-Valued Anal Optim. 2019;1:77–94.
   Google Scholar
• Nguyen S, Dupuis C. An efficient method for computing traffic equilibria in networks with asymmtric transportation costs. Trans Sci. 1984;18:185–201. doi: 10.1287/trsc.18.2.185
   Web of Science ®Google Scholar