On the String Averaging Method for Sparse Common Fixed Points Problems

TL;DR: Yair Censor and Stavros A. Zenios, Oxford University Press, New York, 1997, 539 pp.

TL;DR: In this paper, the authors propose the split common fixed point problem, which requires to find a common fixed points of a family of operators in one space whose image under a linear transformation is a shared fixed point of another operator in the image space.

TL;DR: In this article, the authors propose a split variational inequality problem (SVIP), which is a SIP with the same problem-like structure as the Split Inverse Problem.

TL;DR: A methodology is presented whose aim is to produce automatically for an iterative algorithm of the first kind a "superiorized version" of it that retains its computational efficiency but nevertheless goes a long way towards solving an optimization problem.

Abstract: . A theory of generalized gradients for a general class of functions is developed, as well as a corresponding theory of normals to arbitrary closed sets. It is shown how these concepts subsume the usual gradients and normals of smooth functions and manifolds, and the subdifferentials and normals of convex analysis. A theorem is proved concerning the differentiability properties of a function of the form max{g(x, u):u e if}. This result unifies and extends some theorems of Danskin and others. The results are then applied to obtain a characterization of flow-invariant sets which yields theorems of Bony and Brezis as corollaries.

TL;DR: Foreword Preface Glossary of Symbols 1. Introduction Part I Theory 2. Generalized Distances and Generalized Projections 3. Proximal Minimization with D-Functions Part II Algorithms 4. Penalty Methods, Barrier Methods and Augmented Lagrangians

TL;DR: Yair Censor and Stavros A. Zenios, Oxford University Press, New York, 1997, 539 pp.