Projection Methods: An Annotated Bibliography of Books and Reviews

TL;DR

This paper provides an annotated bibliography of books and reviews on projection methods, highlighting their principles, algorithmic structures, convergence properties, and applications in optimization and scientific problems.

Contribution

It compiles and reviews key literature on projection methods, clarifying their definitions, types, and recent progress in the field.

Findings

Projection methods are effective for feasibility and optimization problems.

They have diverse algorithmic structures suitable for parallel computing.

Recent years have seen significant advancements and successful applications.

Abstract

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.