Projection Methods: An Annotated Bibliography of Books and Reviews

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.

arXiv commentRevised version. Accepted for publication in the journal "Optimization"

References in corpus (1)

• Projection Methods: Swiss Army Knives for Solving Feasibility and Best Approximation Problems with Halfspaces

Cited by in corpus (16)

• Convergence rate analysis for averaged fixed point iterations in the presence of Hölder regularity
• Algorithms and Convergence Results of Projection Methods for Inconsistent Feasibility Problems: A Review
• Circumcentering the Douglas--Rachford method
• Can Linear Superiorization Be Useful for Linear Optimization Problems?
• Sparsity constrained split feasibility for dose-volume constraints in inverse planning of intensity-modulated photon or proton therapy
• A new projection method for finding the closest point in the intersection of convex sets
• A generalized projection-based scheme for solving convex constrained optimization problems
• Optimization on Spheres: Models and Proximal Algorithms with Computational Performance Comparisons
• Infeasibility and error bound imply finite convergence of alternating projections
• Linear Superiorization for Infeasible Linear Programming
• Optimal rates of linear convergence of the averaged alternating modified reflections method for two subspaces
• Finding a best approximation pair of points for two polyhedra
• Alternating conditional gradient method for convex feasibility problems
• Feasibility-based Fixed Point Networks
• Convergence rates for Kaczmarz-type algorithms
• The alternating simultaneous Halpern-Lions-Wittmann-Bauschke algorithm for finding the best approximation pair for two disjoint intersections of convex sets