127
Views
2
CrossRef citations to date
0
Altmetric
Original Articles

Smoothing projected cyclic Barzilai–Borwein method for stochastic linear complementarity problems

, &
Pages 1188-1199 | Received 05 Jun 2014, Accepted 25 Feb 2015, Published online: 15 May 2015

References

  • J. Barzilai and J.M. Borwein, Two-point step size gradient methods, IMA J. Numer. Anal. 8 (1988), pp. 141–148. doi: 10.1093/imanum/8.1.141
  • D.P. Bertsekas, Nonlinear Programming, Athena Scientific, Boston, MA, 1999.
  • E.G. Birgin, J.M. Martínez, and M. Raydan, Nonmonotone spectral projected gradient methods on convex sets, SIAM J. Optim. 10 (2000), pp. 1196–1211. doi: 10.1137/S1052623497330963
  • J.V. Burke, T. Hoheisel, and C. Kanzow, Gradient consistency for integral-convolution smoothing functions, Set-Valued Var. Anal. 21 (2013), pp. 359–376. doi: 10.1007/s11228-013-0235-6
  • P.H. Calamai and J.J. Moré, Projected gradient methods for linearly constrained problems, Math. Program. 39 (1987), pp. 93–116. doi: 10.1007/BF02592073
  • X. Chen, Smoothing methods for nonsmooth, nonconvex minimization, Math. Program. 134 (2012), pp. 71–99. doi: 10.1007/s10107-012-0569-0
  • X. Chen and M. Fukushima, Expected residual minimization method for stochastic linear complementarity problems, Math. Oper. Res. 30 (2005), pp. 1022–1038. doi: 10.1287/moor.1050.0160
  • C. Chen and O.L. Mangasarian, A class of smoothing functions for nonlinear and mixed complementarity problems, Comput. Optim. Appl. 5 (1996), pp. 97–138. doi: 10.1007/BF00249052
  • B. Chen, X. Chen, and C. Kanzow, A penalized Fischer–Burmeister NCP-function, Math. Program. 88 (2000), pp. 211–216. doi: 10.1007/PL00011375
  • X. Chen, C. Zhang, and M. Fukushima, Robust solution of monotone stochastic linear complementarity problems, Math. Program. 117 (2009), pp. 51–80. doi: 10.1007/s10107-007-0163-z
  • F.H. Clarke, Optimization and Nonsmooth Analysis, John Wiley, New York, 1983.
  • Y.H. Dai, On the nonmonotone line search, J. Optim. Theory Appl. 112 (2002), pp. 315–330. doi: 10.1023/A:1013653923062
  • Y.H. Dai and R. Fletcher, Projected Barzilai–Borwein methods for large-scale box-constrained quadratic programming, Numer. Math. 100 (2005), pp. 21–47. doi: 10.1007/s00211-004-0569-y
  • Y.H. Dai, W.W. Hager, K. Schittkowski, and H. Zhang, The cyclic Barzilai–Borwein method for unconstrained optimization, IMA J. Numer. Anal. 26 (2006), pp. 604–627. doi: 10.1093/imanum/drl006
  • F. Facchinei and J.S. Pang, Finite-Dimensional Variational Inequalities and Complementarity Problems, Springer, New York, 2003.
  • H. Fang, X. Chen, and M. Fukushima, Stochastic R0 matrix linear complementarity problems, SIAM J. Optim. 18 (2007), pp. 482–506. doi: 10.1137/050630805
  • A. Fischer, A special Newton-type optimization method, Optimization 24 (1992), pp. 269–284. doi: 10.1080/02331939208843795
  • L. Grippo, F. Lampariello, and S. Lucidi, A nonmonotone line search technique for Newton's method, SIAM J. Numer. Anal. 23 (1986), pp. 707–716. doi: 10.1137/0723046
  • G. Gürkan, A. Yonca Özge, and S.M. Robinson, Sample-path solution of stochastic variational inequalities, Math. Program. 84 (1999), pp. 313–333. doi: 10.1007/s101070050024
  • Y. Huang, H. Liu, and S. Zhou, A Barzilai–Borwein type method for stochastic linear complementarity problems, Numer. Algor. 67 (2014), pp. 477–489. doi: 10.1007/s11075-013-9803-y
  • A.J. Kleywegt, A. Shapiro, and T. Homem-de Mello, The sample average approximation method for stochastic discrete optimization, SIAM J. Optim. 12 (2002), pp. 479–502. doi: 10.1137/S1052623499363220
  • G.H. Lin and M. Fukushima, Stochastic equilibrium problems and stochastic mathematical programs with equilibrium constraints: A survey, Pac. J. Optim. 6 (2010), pp. 455–482.
  • H. Liu, Y. Huang, and X. Li, New reformulation and feasible semismooth Newton method for a class of stochastic linear complementarity problems, Appl. Math. Comput. 217 (2011), pp. 9723–9740. doi: 10.1016/j.amc.2011.04.060
  • H. Liu, Y. Huang, and X. Li, Partial projected Newton method for a class of stochastic linear complementarity problems, Numer. Algor. 58 (2011), pp. 593–618. doi: 10.1007/s11075-011-9472-7
  • H. Liu, X. Li, and Y. Huang, Solving equations via the trust region and its application to a class of stochastic linear complementarity problems, Comput. Math. Appl. 61 (2011), pp. 1646–1664. doi: 10.1016/j.camwa.2011.01.033
  • R.T. Rockafellar, and R. Wets, Variational Analysis, Springer, New York, 1998.
  • S. Ruszczyńskia, Stochastic programming, Handbooks in operations research and management science, Elsevier, Amsterdam, 2003.
  • D. Sun, R.S. Womersley, and H. Qi, A feasible semismooth asymptotically Newton method for mixed complementarity problems, Math. Program. 94 (2002), pp. 167–187. doi: 10.1007/s10107-002-0305-2
  • C. Zhang and X. Chen, Smoothing projected gradient method and its application to stochastic linear complementarity problems, SIAM J. Optim. 20 (2009), pp. 627–649. doi: 10.1137/070702187
  • H. Zhang and W.W. Hager, A nonmonotone line search technique and its application to unconstrained optimization, SIAM J. Optim. 14 (2004), pp. 1043–1056. doi: 10.1137/S1052623403428208
  • G.L. Zhou and L. Caccetta, Feasible semismooth Newton method for a class of stochastic linear complementarity problems, J. Optim. Theory Appl. 139 (2008), pp. 379–392. doi: 10.1007/s10957-008-9406-2

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.