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求解拟变分不等式问题的一种投影算法 被引量：4

A Projection-like Algorithm for the Quasi-variational Inequality Problem
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摘要 拟变分不等式问题在经济、工程、最优化和控制等领域都有着广泛的应用,目前,对拟变分不等式问题的研究还处于初级阶段.在本文中,我们利用梯度投影技术,给出了一种求解拟变分不等式问题的投影类算法,证明了该算法的全局收敛性,并给出了数值试验结果. The quasi-variational inequality（QVI）theory has been applied extensively in the study of a large numbers of problems arising in economics,engineering mechanics,optimization and control,etc.The study of the QVI to date is in its infancy at best.In this paper,using the gradient projection technique,we present a projection-like algorithm for the quasi-variational inequality problem.It is proved that the proposed algorithm is globally convergent.Preliminary numerical results are also reported.
作者 屈彪 张善美
机构地区 曲阜师范大学运筹与管理学院 日照校区图书馆
出处 《应用数学学报》 CSCD 北大核心 2008年第5期922-928,共7页 Acta Mathematicae Applicatae Sinica
基金 国家自然科学基金(10701047，10571106)资助项目
关键词 拟变分不等式 算法 收敛 quasi-variational inequality problem algorithm convergence
分类号 O221.2 [理学—运筹学与控制论]
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参考文献10

  • 1Harker P T. Generalized Nash Games and Quasi-variational Inequalities. European Journal of Operational Research, 1991, 54:81-94.
  • 2Facchinei F, Pang J S. Finite-dimensional Variational Inequality and Complementarity Problems. New York: Springer-Verlag, 2003.
  • 3Chart D, Pang J S. The Generalized Quasi-variational Inequality Problem. Mathematics of Operations Research, 1982, 7:211-222.
  • 4Yao J C. The Generalized Quasi-variational Inequality Problem with Applications. Journal of Mathematical Analysis and Applications, 1991, 158:139-160.
  • 5Kocvara M, Outrata J V. On a Class of Quasi-variational Inequalities. Optimization Methods and Software, 1995, 5:275-295.
  • 6Pang J S, Fukushima M. Quasi-variational Inequalities, Generalized Nash Equilibria, and Multi-leader- follower Games. Computational Management Science, 2005, 2:21-56.
  • 7Zarantonello E H. Projections on Convex Sets in Hilbert Space and Spectral Theory. Contributions to Nonlinear Functional Analysis, ed. E. H. Zarantonello. New York: Academic Press, 1971.
  • 8Toint Ph L. Global Convergence of a Class of Trust Region Methods for Nonconvex Minimization in Hilbert Space. IMA Journal of Numerical Analysis, 1988, 8:231-252.
  • 9Gafni E M, Bertsekas D P. Two-metric Projection Problems and Descent Methods for Asymmetric Variational Inequality Problems. Mathematical Programming, 1984, 53:99-110.
  • 10Outrata J, Zowe J. A Numerical Approach to Optimization Problems with Vatiational Inequality Constraints. Mathematical Programming, 1995, 68:105-130.

同被引文献24

  • 1Hartman P, Stampacchia G. On some nonlinear elliptic differential functional equations. Aeta Math., 1966, 115: 153-188.
  • 2Facchinei F, Pang J S. Finite-Dimensional Variational Inequality and Complementarity Problems. New York: Springer-Verlag, 2003.
  • 3Solodov M V, Svaiter B F. A new projection method for variational inequality problems. SIMJ J. Control Optim., 1999, 37: 765-776.
  • 4Wang Y J, Xiu N H, Wang C W. Unified framework of extragradient-type methods for pseu- domonotone variational inequalities. J. Optim. Theory Appl., 2001, 111(3): 641456.
  • 5Kocvara M, Outrata J V. On a class of quasi-variational inequalities. Optim. Methods Soft., 1995, 5: 275-295.
  • 6Yao J C. The generalized quasi-variational inequality problem with applications. J. Math. Anal. Appl., 1991, 158: 139-160.
  • 7Pang J S, Fukushima M. Quasi-variational inequalities, generalized nash equalibria, and multi- leader-follower games. Comput. Manag. Scien., 2005, 2: 21-56.
  • 8Noor M A. On quasi-variational inequalities. J. King Saud Univ. Scien., 2012, 24: 81-88.
  • 9He Y R. A new double projection algorithm for variational inequalities. J. Comput. Appl. Math., 2006, 185: 166-173.
  • 10Harker P T. Generalized Nash Games and Quasi-variational Inequalities[J].European Journal of Operational Research,1991,(01):81-94.

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应用数学学报
2008年 第5期

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