A note on the paper by Eckstein and svaiter on "general projective splitting methods for sums of maximal monotone operators"

SIAM Journal on Control and Optimization

Volumn 48, Issue 4, 2009, Pages 2513-2515

  Bauschke, Heinz H ^a  

^a UNIVERSITY OF BRITISH COLUMBIA   (Canada)

Author keywords

Firmly nonexpansive mapping; Maximal monotone operator; Nonexpansive mapping; Proximal algorithm; Splitting algorithm

Indexed keywords

FIRMLY NONEXPANSIVE MAPPING; MAXIMAL MONOTONE OPERATORS; NONEXPANSIVE MAPPINGS; PROXIMAL ALGORITHM; SPLITTING ALGORITHMS;

EID: 77955851047     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/090759690     Document Type: Article

References (14)

1. R.S. BURACHIK and A.N. IUSEM, Set-Valued Mappings and Enlargements of Monotone Operators, Springer-Verlag, Berlin, 2008.
2. P.L. COMBETTES, Iterative construction of the resolvent of a sum of maximal monotone operators, J. Convex Anal., 16 (2009).
3. J.B. CONWAY, A Course in Functional Analysis, 2nd ed., Springer-Verlag, Berlin, 1990.
4. J. ECKSTEIN, Splitting methods for monotone operators with applications to parallel optimization, Ph.D. thesis, Department of Civil Engineering, Massachusetts Institute of Technology, Boston, 1989.
5. J. ECKSTEIN and D.P. BERTSEKAS, On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators, Math. Program., 55 (1992), pp. 293-318.
6. J. ECKSTEIN and M.C. FERRIS, Operator splitting methods for monotone affine variational inequalities, with a parallel application to optimal control, INFORMS J. Comput., 10 (1998), pp. 218-235.
7. J. ECKSTEIN and B.F. SVAITER, General projective splitting methods for sums of maximal monotone operators, SIAM J. Control Optim., 48 (2009), pp. 787-811.
8. K. GOEBEL and W.A. KIRK, Topics in Metric Fixed Point Theory, Cambridge University Press, London, 1990.
9. K. GOEBEL and S. REICH, Uniform Convexity, Hyperbolic Geometry, and Nonexpansive Mappings, Marcel Dekker, New York, 1984.
10. J. LAWRENCE and J.E. SPINGARN, On fixed points of non-expansive piecewise isometric mappings, Proc. London Math. Soc., 55 (1987), pp. 605-624.
11. R.T. ROCKAFELLAR and R.J-B WETS, Variational Analysis, 2nd printing, Springer-Verlag, Berlin, 2004.
12. S. SIMONS, Minimax and Monotonicity, Springer-Verlag, Berlin, 1998.
13. S. SIMONS, From Hahn-Banach to Monotonicity, Springer-Verlag, Berlin, 2008.
14. C. ZALINESCU, Convex Analysis in General Vector Spaces, World Scientific Publishing, River Edge, NJ, 2002.