Primal Space Necessary Characterizations of Transversality Properties

This paper continues the study of general nonlinear transversality properties of collections of sets and focuses on primal space necessary (in some cases also sufficient) characterizations of the properties. We formulate geometric, metric and slope characterizations, particularly in the convex setting. The Holder case is given a special attention. Quantitative relations between the nonlinear transversality … Read more

Geometric and Metric Characterizations of Transversality Properties

This paper continues the study of ‘good arrangements’ of collections of sets near a point in their intersection. Our aim is to clarify the relations between various quantitative geometric and metric characterizations of the transversality properties of collections of sets and the corresponding regularity properties of set-valued mappings. We expose all the parameters involved in … Read more

Nonlinear Transversality Properties of Collections of Sets: Dual Space Necessary Characterizations

This paper continues the study of ‘good arrangements’ of collections of sets in normed vector spaces near a point in their intersection. Our aim is to study general nonlinear transversality properties. We focus on dual space (subdifferential and normal cone) necessary characterizations of these properties. As an application, we provide dual necessary and sufficient conditions … Read more

Inexact alternating projections on nonconvex sets

Given two arbitrary closed sets in Euclidean space, a simple transversality condition guarantees that the method of alternating projections converges locally, at linear rate, to a point in the intersection. Exact projection onto nonconvex sets is typically intractable, but we show that computationally-cheap inexact projections may suffice instead. In particular, if one set is defined … Read more

Alternating projections and coupling slope

We consider the method of alternating projections for finding a point in the intersection of two possibly nonconvex closed sets. We present a local linear convergence result that makes no regularity assumptions on either set (unlike previous results), while at the same time weakening standard transversal intersection assumptions. The proof grows out of a study … Read more