Related papers: Constraint reduction reformulations for projection…
Feasibility problem aims to find a common point of two or more closed (convex) sets whose intersection is nonempty. In the literature, projection based algorithms are widely adopted to solve the problem, such as the method of alternating…
In this paper, we study the generalized Douglas-Rachford algorithm and its cyclic variants which include many projection-type methods such as the classical Douglas-Rachford algorithm and the alternating projection algorithm. Specifically,…
The Douglas-Rachford method, a projection algorithm designed to solve continuous optimization problems, forms the basis of a useful heuristic for solving combinatorial optimization problems. In order to successfully use the method, it is…
In this paper we present two Douglas-Rachford inspired iteration schemes which can be applied directly to N-set convex feasibility problems in Hilbert space. Our main results are weak convergence of the methods to a point whose nearest…
The Douglas-Rachford algorithm is a simple yet effective method for solving convex feasibility problems. However, if the underlying constraints are inconsistent, then the convergence theory is incomplete. We provide convergence results when…
This paper proposes an algorithm for solving structured optimization problems, which covers both the backward-backward and the Douglas-Rachford algorithms as special cases, and analyzes its convergence. The set of fixed points of the…
Many iterative methods for solving optimization or feasibility problems have been invented, and often convergence of the iterates to some solution is proven. Under favourable conditions, one might have additional bounds on the distance of…
This paper presents a reformulation of the construction of nonseparable multiresolution quaternion-valued wavelets on the plane as a feasibility problem. The constraint sets in the feasibility problem are derived from the standard…
The Douglas-Rachford projection algorithm is an iterative method used to find a point in the intersection of closed constraint sets. The algorithm has been experimentally observed to solve various nonconvex feasibility problems which…
In this paper, we propose a new algorithm combining the Douglas-Rachford (DR) algorithm and the Frank-Wolfe algorithm, also known as the conditional gradient (CondG) method, for solving the classic convex feasibility problem. Within the…
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 solved numerically via convex heuristics or nicely-behaved nonconvex…
The Douglas-Rachford algorithm is a classical and very successful method for solving optimization and feasibility problems. In this paper, we provide novel conditions sufficient for finite convergence in the context of convex feasibility…
Different notions on regularity of sets and of collection of sets play an important role in the analysis of the convergence of projection algorithms in nonconvex scenarios. While some projection algorithms can be applied to feasibility…
In this paper we propose a product space reformulation to transform monotone inclusions described by finitely many operators on a Hilbert space into equivalent two-operator problems. Our approach relies on Pierra's classical reformulation…
The Douglas-Rachford splitting algorithm is a classical optimization method that has found many applications. When specialized to two normal cone operators, it yields an algorithm for finding a point in the intersection of two convex sets.…
Motivated by nonconvex, inconsistent feasibility problems in imaging, the relaxed alternating averaged reflections algorithm, or relaxed Douglas-Rachford algorithm (DR$\lambda$), was first proposed over a decade ago. Convergence results for…
We present the convergence analysis of convex combination of the alternating projection and Douglas-Rachford operators for solving the phase retrieval problem. New convergence criteria for iterations generated by the algorithm are…
We study the cyclic relaxed Douglas-Rachford algorithm for possibly nonconvex, and inconsistent feasibility problems. This algorithm can be viewed as a convex relaxation between the cyclic Douglas-Rachford algorithm first introduced by…
The main challenge of nonconvex optimization is to find a global optimum, or at least to avoid ``bad'' local minima and meaningless stationary points. We study here the extent to which algorithms, as opposed to optimization models and…
We show that a broad range of convex optimization algorithms, including alternating projection, operator splitting, and multiplier methods, can be systematically derived from the framework of subspace correction methods via convex duality.…