Regularized gradient-projection methods for equilibrium and constrained convex minimization problems

被引：0
作者：
Ming Tian
Li-Hua Huang
机构：
[1] Civil Aviation University of China,College of Science
来源：
Journal of Inequalities and Applications | / 2013卷
关键词：
iterative method; constrained convex minimization; equilibrium; fixed point; variational inequality;
D O I：
暂无
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学科分类号：
摘要：
In this article, based on Marino and Xu’s method, an iterative method which combines the regularized gradient-projection algorithm (RGPA) and the averaged mappings approach is proposed for finding a common solution of equilibrium and constrained convex minimization problems. Under suitable conditions, it is proved that the sequences generated by implicit and explicit schemes converge strongly. The results of this paper extend and improve some existing results.
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  • [1] Bertsekas DP(1982)Projection methods for variational inequalities with applications to the traffic assignment problem Math. Program. Stud 17 139-159
  • [2] Gafni EM(2004)Solving non-additive traffic assignment problems, a descent method for cocoercive variational inequalities Eur. J. Oper. Res 159 529-544
  • [3] Han D(1996)On projection algorithms for solving convex feasibility problems SIAM Rev 38 367-426
  • [4] Lo HK(2004)A unified treatment of some iterative algorithms in signal processing and image reconstruction Inverse Probl 20 103-120
  • [5] Bauschke H(2004)Solving monotone inclusions via compositions of nonexpansive averaged operators Optimization 53 475-504
  • [6] Borwein J(2011)Averaged mappings and the gradient-projection algorithm J. Optim. Theory Appl 150 360-378
  • [7] Byrne C(2007)Viscosity approximation methods for equilibrium problems and fixed point problems in Hilbert spaces J. Math. Anal. Appl 331 506-515
  • [8] Combettes PL(2005)Equilibrium programming in Hilbert spaces J. Nonlinear Convex Anal 6 117-136
  • [9] Xu HK(1997)Equilibrium programming using proximal-like algorithms Math. Program 78 29-41
  • [10] Takahashi S(2011)An explicit method for systems of equilibrium problems and fixed points of infinite family of nonexpansive mappings J. Comput. Appl. Math 235 4128-4139
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