Monotone Operators and Splitting Methods: An Introduction and Some New Results
Jonathan Eckstein (joint work with B.F. Svaiter, IMPA (Rio de Janeiro))
Rutgers University (MSIS Department and RUTCOR)
On sabbatical at Princeton University (ORFE Department)

Abstract: Set-valued monotone operators on Hilbert spaces are fundamental mathematical objects closely related to convex sets, convex functions, and nonexpansive maps. The first part of this talk provides a general introduction to maximal monotone operators, some of their applications, and the notion of splitting algorithms for finding roots of sums of such operators. The second part of the talk presents some recent theoretical results on splitting algorithms that are far more general and flexible than traditional ones. These new, "projective" splitting methods use a decomposition procedure to construct separating hyperplanes for an "extended" solution set obtained through a product-space construction.