On the String Averaging Method for Sparse Common Fixed Points Problems

作者: Yair Censor , Alexander Segal

DOI: 10.1111/J.1475-3995.2008.00684.X

关键词:

摘要: We study the common fixed points problem for class of directed operators. This is important because many commonly used nonlinear operators in convex optimization belong to it. propose a definition sparseness family and investigate string-averaging algorithmic scheme that favorably handles when sparse. The feasibility treated as special case new subgradient projections obtained.

参考文章(28)
Yair Al Censor, Stavros A. Zenios, Parallel Optimization: Theory, Algorithms, and Applications ,(1997)
Hyang-Joo Rhee, AN APPLICATION OF THE STRING AVERAGING METHOD TO ONE-SIDED BEST SIMULTANEOUS APPROXIMATION Pure and Applied Mathematics. ,vol. 10, pp. 49- 56 ,(2003)
Y. Censor, T. Elfving, G.T. Herman, Averaging Strings of Sequential Iterations for Convex Feasibility Problems Studies in Computational Mathematics. ,vol. 8, pp. 101- 113 ,(2001) , 10.1016/S1570-579X(01)80009-4
Patrick L. Combettes, Quasi-Fejérian Analysis of Some Optimization Algorithms Studies in Computational Mathematics. ,vol. 8, pp. 115- 152 ,(2001) , 10.1016/S1570-579X(01)80010-0
Yair Censor, Tommy Elfving, Block-Iterative Algorithms with Diagonally Scaled Oblique Projections for the Linear Feasibility Problem SIAM Journal on Matrix Analysis and Applications. ,vol. 24, pp. 40- 58 ,(2002) , 10.1137/S089547980138705X
John M. Dye, Simeon Reich, Unrestricted iterations of nonexpansive mappings in Hilbert space Nonlinear Analysis-theory Methods & Applications. ,vol. 18, pp. 199- 207 ,(1992) , 10.1016/0362-546X(92)90094-U
Yair Censor, Dan Gordon, Rachel Gordon, Component averaging: An efficient iterative parallel algorithm for large and sparse unstructured problems parallel computing. ,vol. 27, pp. 777- 808 ,(2001) , 10.1016/S0167-8191(00)00100-9
J. T. Betts, P. D. Frank, A sparse nonlinear optimization algorithm Journal of Optimization Theory and Applications. ,vol. 82, pp. 519- 541 ,(1994) , 10.1007/BF02192216
Felix E. Browder, Convergence theorems for sequences of nonlinear operators in Banach spaces Mathematische Zeitschrift. ,vol. 100, pp. 201- 225 ,(1967) , 10.1007/BF01109805
G. Crombez, FINDING COMMON FIXED POINTS OF A CLASS OF PARACONTRACTIONS Acta Mathematica Hungarica. ,vol. 103, pp. 233- 241 ,(2004) , 10.1023/B:AMHU.0000028410.94541.FB