AAM  >> Vol. 4 No. 1 (February 2015)

    求解拟变分不等式问题的一种外梯度算法
    An Extragradient Algorithm for Quasi-Variat-Ional Inequality Problem

  • 全文下载: PDF(1093KB) HTML   XML   PP.70-75   DOI: 10.12677/AAM.2015.41009  
  • 下载量: 987  浏览量: 3,728   国家自然科学基金支持

作者:  

袁媛媛,张文伟,屈 彪:曲阜师范大学管理学院,山东 日照

关键词:
拟变分不等式投影外梯度Quasi-Variational Inequality Projection Extragradient

摘要:

本文给出了求解拟变分不等式问题的一种投影算法,在算法的第二次投影步中,把到一般闭凸集上的投影松弛为到半空间的投影,这在一定程度上减少了计算的难度。该算法的全局收敛性得到证明。

In this paper, we present a projection-like algorithm for solving the quasi-variational inequality problem. In the second projection step of the algorithm, we replace the orthogonal projection onto a general closed convex set with a projection onto a halfspace, which reduces the difficulty of cal-culation to some extent. The global convergence of the algorithm is given. 

文章引用:
袁媛媛, 张文伟, 屈彪. 求解拟变分不等式问题的一种外梯度算法[J]. 应用数学进展, 2015, 4(1): 70-75. http://dx.doi.org/10.12677/AAM.2015.41009

参考文献

[1] Harker, P. (1991) Generalized Nash games and quasi-variational inequalities. European Journal of Operational Research, 54, 81-94.
[2] Pang, J.S. and Fukushima, M. (2005) Quasi-variational inequalities, generalized Nash equilibria and multileader-Fol- lower game. Computational Management Science, 1, 21-56.
[3] Zhang, J.Z., Qu, B. and Xiu, N.H. (2010) Some projection-like methods for the generalized Nash equilibria. Computational Optimization and Applications, 45, 89-109.
[4] Han, D., Zhang, H., Qian, G. and Xu, L. (2012) An improved two-step method for solving generalized Nash equilibrium problems. European Journal of Operational Research, 216, 613-623.
[5] 屈彪, 张善美 (2008) 求解拟变分不等式问题的一种投影算法. 应用数学学报, 5, 922-928.
[6] Censor, Y., Gibali, A. and Reich, S. (2011) The subgradient extragradient method for solving variational inequlities in Hilbert space. Journal of Optimization Theory and Applications, 148, 318-335.
[7] Zarantonello, E.H. (1971) Projections on convex sets in Hilbert space and spectral theory. In: Zarantonello, E.H., Ed., Contributions to Nonlinear Functional Analysis, American Academic Press, New York, 19-32.
[8] Gafni, E.M. and Bertsekas, D.P. (1984) Two-metric projection problems and descent methods for asymmetric variational inequality problems. Math. Program, 53, 99-110.
[9] Haker, P.T. (1991) Generalized Nash games and quasi-variational inequalities. European Journal of Operational Research, 54, 81-94.
[10] Outrata, J. and Zowe, J. (1995) A numerical approach to optimization problems with variational inequality constraints. Mathematical Programming, 68, 105-130.