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Research Article

Distributionally robust expected residual minimization for stochastic variational inequality problems

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Pages 756-780 | Received 09 Dec 2021, Accepted 08 Jan 2023, Published online: 06 Feb 2023

References

  • R.P. Agdeppa, N. Yamashita, and M. Fukushima, Convex expected residual models for stochastic affine variational inequality problems and its application to the traffic equilibrium problem, Pac. J. Optim. 6 (2010), pp. 3–19.
  • A. Ben-Tal and A. Nemirovski, Robust solutions of linear programming problems contaminated with uncertain data, Math. Program. 88 (2000), pp. 411–424.
  • A. Ben-Tal and A. Nemirovski, Robust optimization–methodology and applications, Math. Program. 92 (2002), pp. 453–480.
  • K. Bertsimas, K. Natarajan, and C.P. Teo, Persistence in discrete optimization under data uncertainty, Math. Program. 108 (2006), pp. 251–274.
  • X. Chen and M. Fukushima, Expected residual minimization method for stochastic linear complementarity problems, Math. Oper. Res. 30 (2005), pp. 1022–1038.
  • X. Chen, T.K. Pong, and R.J.B Wets, Two-stage stochastic variational inequalities: An ERM-solution procedure, Math. Program. 165 (2017), pp. 71–111.
  • X. Chen, R.J.B. Wets, and Y. Zhang, Stochastic variational inequalities: Residual minimization smoothing sample average approximations, SIAM J. Optim. 22 (2012), pp. 649–673.
  • E. Delage and Y. Ye, Distributionally robust optimization under moment uncertainty with application to data-driven problems, Oper. Res. 58 (2010), pp. 595–612.
  • K. Derinkuyu and M.Ç. Pınar, On the S-procedure and some variants, Math. Methods Oper. Res. 64 (2006), pp. 55–77.
  • M. Fukushima, Equivalent differentiable optimization problems and descent methods for asymmetric variational inequality problems, Math. Program. 53 (1992), pp. 99–110.
  • S. Guo and H. Xu, Statistical robustness in utility preference robust optimization models, Math. Program. 190 (2021), pp. 679–720.
  • G. Gürkan, A.Y. Özge, and S.M. Robinson, Sample-path solution of stochastic variational inequalities, Math. Program. 84 (1999), pp. 313–333.
  • J. Jiang and S. Li, Statistical robustness of two-stage stochastic variational inequalities, Optim. Lett. 16 (2022), pp. 2591–2605.
  • V. Krätschmer, A. Schied, and H. Zähle, Qualitative and infinitesimal robustness of tail-dependent statistical functionals, J. Multivar. Anal. 103 (2012), pp. 35–47.
  • M.J. Luo and G.H. Lin, Expected residual minimization method for stochastic variational inequality problems, J. Optim. Theory Appl. 140 (2009), pp. 103–116.
  • M.J. Luo and G.H. Lin, Convergence results of the ERM method for nonlinear stochastic variational inequality problems, J. Optim. Theory Appl. 142 (2009), pp. 569–581.
  • S. Mehrotra and D. Papp, A cutting surface algorithm for semi-infinite convex programming with an application to moment robust optimization, SIAM J. Optim. 24 (2014), pp. 1670–1697.
  • I. Pólik and T. Terlaky, A survey of the S-lemma, SIAM Rev. 49 (2007), pp. 371–418.
  • H. Rahimian and S. Mehrotra, Frameworks and results in distributionally robust optimization, Open J. Math. Optim. 3 (2022), pp. 1–85.
  • A. Shapiro, First and second order analysis of nonlinear semidefinite programs, Math. Program. 77 (1997), pp. 301–320.
  • J.F. Sturm and S. Zhang, On cones of nonnegative quadratic functions, Math. Oper. Res. 28 (2003), pp. 246–267.
  • H. Xu, Y. Liu, and H. Sun, Distributionally robust optimization with matrix moment constraints: Lagrange duality and cutting plane methods, Math. Program. 169 (2018), pp. 489–529.
  • H. Yamashita and H. Yabe, A primal-dual interior point method for nonlinear optimization over second-order cones, Optim. Methods Softw. 24 (2009), pp. 407–426.
  • H. Yamashita, H. Yabe, and K. Harada, A primal-dual interior point method for nonlinear semidefinite programming, Math. Program. 135 (2012), pp. 89–121.
  • L. Zhu, B. Yu, and L. Xu, The distributionally robust complementarity problem, Optim. Methods Softw. 32 (2017), pp. 650–668.

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