Set intersection problems: Integrating projection and quadratic programming algorithms
Abstract
Abstract. The Set Intersection Problem (SIP) is the problem of finding a point in the intersection of convex sets. This problem is typically solved by the method of alternating projections. To accelerate the convergence, the idea of using Quadratic Programming (QP) to project a point onto the intersection of halfspaces generated by the projection process was discussed in earlier papers. This paper looks at how one can integrate projection algorithms together with an active set QP algorithm. As a byproduct of our analysis, we show how to accelerate an SIP algorithm involving box constraints, and how to extend a version of the Algebraic Reconstruction Technique (ART) while preserving finite convergence. Lastly, the warmstart property of active set QP algorithms is a valuable property for the problem of projecting onto the intersection of convex sets.
Cite
@article{arxiv.1307.0053,
title = {Set intersection problems: Integrating projection and quadratic programming algorithms},
author = {C. H. Jeffrey Pang},
journal= {arXiv preprint arXiv:1307.0053},
year = {2015}
}
Comments
25 pages, 7 figures. This submission is completely different from the last submission. I now feel that the last submission didn't develop the idea of integrating the dual active set quadratic programming algorithm of Goldfarb and Idnani to projection algorithms well enough, and that this submission has developed the idea and worked out relevant theoretical issues much better