  Projections onto sets are used in a wide variety of methods in optimization
theory but not every method that uses projections really belongs to the class
of projection methods as we mean it here. Here projection methods are iterative
algorithms that use projections onto sets while relying on the general
principle that when a family of (usually closed and convex) sets is present
then projections (or approximate projections) onto the given individual sets
are easier to perform than projections onto other sets (intersections, image
sets under some transformation, etc.) that are derived from the given family of
individual sets. Projection methods employ projections (or approximate
projections) onto convex sets in various ways. They may use different kinds of
projections and, sometimes, even use different projections within the same
algorithm. They serve to solve a variety of problems which are either of the
feasibility or the optimization types. They have different algorithmic
structures, of which some are particularly suitable for parallel computing, and
they demonstrate nice convergence properties and/or good initial behavior
patterns. This class of algorithms has witnessed great progress in recent years
and its member algorithms have been applied with success to many scientific,
technological, and mathematical problems. This annotated bibliography includes
books and review papers on, or related to, projection methods that we know
about, use, and like. If you know of books or review papers that should be
added to this list please contact us.
