This monograph is about a class of optimization algorithms called proximal algorithms. Much
like Newton's method is a standard tool for solving unconstrained smooth optimization …

We consider the problem of finding a best approximation pair, ie, two points which achieve
the minimum distance between two closed convex sets in a Hilbert space. When the sets …

We model a problem motivated by road design as a feasibility problem. Projections onto the
constraint sets are obtained, and projection methods for solving the feasibility problem are …

A novel approach for solving the general absolute value equation A x+ B| x|= c where A, B∈
IR m× n and c∈ IR m is presented. We reformulate the equation as a nonconvex feasibility …

The convex feasibility problem under consideration is to find a common point of a countable
family of closed affine subspaces and convex sets in a Hilbert space. To solve such …

The problem of finding a vector with the fewest nonzero elements that satisfies an
underdetermined system of linear equations is an NP-complete problem that is typically …

We systematically study the optimal linear convergence rates for several relaxed alternating
projection methods and the generalized Douglas-Rachford splitting methods for finding the …

Circular cone includes second-order cone as a special case when the rotation angle is 45
degree. This paper gives an insight on circular cone, in which we describe the tangent cone …

We study the convergence of specific inexact alternating projections for two non-convex sets
in a Euclidean space. The $\sigma $-quasioptimal metric projection ($\sigma\geq 1$) of a …

Solving feasibility problems is a central task in mathematics and the applied sciences. One
particularly successful method is the Douglas--Rachford algorithm. In this paper, we provide …