Journal ArticleDOI
Solving proximal split feasibility problems without prior knowledge of operator norms
Reads0
Chats0
TLDR
In this paper, a split proximal algorithm with a way of selecting the step-sizes such that its implementation does not need any prior information about the operator norm is proposed.Abstract:
In this paper our interest is in investigating properties and numerical solutions of Proximal Split feasibility Problems. First, we consider the problem of finding a point which minimizes a convex function \(f\) such that its image under a bounded linear operator \(A\) minimizes another convex function \(g\). Based on an idea introduced in Lopez (Inverse Probl 28:085004, 2012), we propose a split proximal algorithm with a way of selecting the step-sizes such that its implementation does not need any prior information about the operator norm. Because the calculation or at least an estimate of the operator norm \(\Vert A\Vert \) is not an easy task. Secondly, we investigate the case where one of the two involved functions is prox-regular, the novelty of this approach is that the associated proximal mapping is not nonexpansive any longer. Such situation is encountered, for instance, in numerical solution to phase retrieval problem in crystallography, astronomy and inverse scattering Luke (SIAM Rev 44:169–224, 2002) and is therefore of great practical interest.read more
Citations
More filters
Journal ArticleDOI
Convergence analysis for the proximal split feasibility problem using an inertial extrapolation term method
Yekini Shehu,Olaniyi S. Iyiola +1 more
TL;DR: In this article, a proximal split feasibility algorithm with an additional inertial extrapolation term was proposed for solving the proximal-split feasibility problem under weaker conditions on the step sizes, where the convex and lower semi continuous objective functions are assumed to be non-smooth.
Journal ArticleDOI
A modified Halpern algorithm for approximating a common solution of split equality convex minimization problem and fixed point problem in uniformly convex Banach spaces
TL;DR: In this article, a modified Halpern algorithm was proposed for approximating a common solution of split equality convex minimization problem and split-equality fixed-point problem for Bregman quasi-nonexpansive mappings in p-uniformly convex and uniformly smooth Banach spaces.
Journal ArticleDOI
Convergence analysis for proximal split feasibility problems and fixed point problems
Yekini Shehu,F. U. Ogbuisi +1 more
TL;DR: In this paper, the authors introduce iterative algorithms and prove their strong convergence for solving proximal split feasibility problems and fixed point problems for pseudocontractive mappings in Hilbert spaces.
Journal ArticleDOI
Viscosity S-iteration method with inertial technique and self-adaptive step size for split variational inclusion, equilibrium and fixed point problems
Journal ArticleDOI
Iterative approximation of solutions for proximal split feasibility problems
TL;DR: A viscosity type algorithm for solving proximal split feasibility problems and the strong convergence of the sequences generated by the authors' iterative schemes in Hilbert spaces are introduced.
References
More filters
Book
A wavelet tour of signal processing
TL;DR: An introduction to a Transient World and an Approximation Tour of Wavelet Packet and Local Cosine Bases.
Book
An introduction to optimization
TL;DR: This review discusses mathematics, linear programming, and set--Constrained and Unconstrained Optimization, as well as methods of Proof and Some Notation, and problems with Equality Constraints.
Journal ArticleDOI
Monotone Operators and the Proximal Point Algorithm
TL;DR: In this paper, the proximal point algorithm in exact form is investigated in a more general form where the requirement for exact minimization at each iteration is weakened, and the subdifferential $\partial f$ is replaced by an arbitrary maximal monotone operator T.
Journal ArticleDOI
Signal recovery by proximal forward-backward splitting ∗
TL;DR: It is shown that various inverse problems in signal recovery can be formulated as the generic problem of minimizing the sum of two convex functions with certain regularity properties, which makes it possible to derive existence, uniqueness, characterization, and stability results in a unified and standardized fashion for a large class of apparently disparate problems.
Related Papers (5)
A multiprojection algorithm using Bregman projections in a product space
Yair Censor,Tommy Elfving +1 more