616 citations · 956 across the 24 of their papers we have counts for
27 papers
Nonlinear three-operator splitting algorithms with momentum for monotone inclusions
Liqian Qin, Aviv Gibali, Cuijie Zhang +1
In this paper, we introduce three novel splitting algorithms for solving structured monotone inclusion problems involving the sum of a maximally monotone operator, a monotone and L…
Plug-and-play superiorization
Jon Henshaw, Aviv Gibali, Thomas Humphries
The superiorization methodology (SM) is an optimization heuristic in which an iterative algorithm, which aims to solve a particular problem, is ``superiorized'' to promote solution…
Approaches to iterative algorithms for solving nonlinear equations with an application in tomographic absorption spectroscopy
F. J. Aragón-Artacho, W. Cai, Y. Censor +3
In this paper we propose an approach for solving systems of nonlinear equations without computing function derivatives. Motivated by the application area of tomographic absorption…
Superiorized Regularization of Inverse Problems
Aviv Gibali, Markus Haltmeier
Inverse problems are characterized by their inherent non-uniqueness and sensitivity with respect to data perturbations. Their stable solution requires the application of regulariza…
Levitin-Polyak Well-posedness for Split Equilibrium Problems
Soumitra Dey, Aviv Gibali, Simeon Reich
The notion of well-posedness has drawn the attention of many researchers in the field of nonlinear analysis, as it allows to explore problems in which exact solutions are not known…
The superiorization method with restarted perturbations for split minimization problems with an application to radiotherapy treatment planning
Francisco J. Aragón-Artacho, Yair Censor, Aviv Gibali +1
In this paper we study the split minimization problem that consists of two constrained minimization problems in two separate spaces that are connected via a linear operator that ma…
Unrestricted Douglas-Rachford algorithms for solving convex feasibility problems in Hilbert space
Kay Barshad, Aviv Gibali, Simeon Reich
In this work we focus on the convex feasibility problem (CFP) in Hilbert space. A specific method in this area that has gained a lot of interest in recent years is the Douglas-Rach…
Feasibility-based Fixed Point Networks
Howard Heaton, Samy Wu Fung, Aviv Gibali +1
Inverse problems consist of recovering a signal from a collection of noisy measurements. These problems can often be cast as feasibility problems; however, additional regularizatio…
Non-Convex Split Feasibility Problems: Models, Algorithms and Theory
Aviv Gibali, Shoham Sabach, Sergey Voldman
In this paper, we propose a catalog of iterative methods for solving the Split Feasibility Problem in the non-convex setting. We study four different optimization formulations of t…
Computing Dynamic User Equilibrium on Large-Scale Networks Without Knowing Global Parameters
Duong Viet Thong, Aviv Gibali, Mathias Staudigl +1
Dynamic user equilibrium (DUE) is a Nash-like solution concept describing an equilibrium in dynamic traffic systems over a fixed planning period. DUE is a challenging class of equi…
Dynamic string-averaging CQ-methods for the split feasibility problem with percentage violation constraints arising in radiation therapy treatment planning
Mark Brooke, Yair Censor, Aviv Gibali
In this paper we study a feasibility-seeking problem with percentage violation constraints. These are additional constraints, that are appended to an existing family of constraints…
Outer Approximation Methods for Solving Variational Inequalities Defined over the Solution Set of a Split Convex Feasibility Problem
Andrzej Cegielski, Aviv Gibali, Simeon Reich +1
We study variational inequalities which are governed by a strongly monotone and Lipschitz continuous operator over a closed and convex set . We assume that $S=C\cap A^{-1}(Q…
Accelerating two projection methods via perturbations with application to Intensity-Modulated Radiation Therapy
E. Bonacker, A. Gibali, K. -H. Küfer
Constrained convex optimization problems arise naturally in many real-world applications. One strategy to solve them in an approximate way is to translate them into a sequence of c…
A generalized projection-based scheme for solving convex constrained optimization problems
Aviv Gibali, Karl-Heinz Küfer, Daniel Reem +1
In this paper we present a new algorithmic realization of a projection-based scheme for general convex constrained optimization problem. The general idea is to transform the origin…
A modified subgradient extragradient method for solving the variational inequality problem
Qiao-Li Dong, Dan Jiang, Aviv Gibali
The subgradient extragradient method for solving the variational inequality (VI) problem, which is introduced by Censor et al. \cite{CGR}, replaces the second projection onto the f…
The Cyclic Douglas-Rachford Algorithm with r-sets-Douglas-Rachford Operators
Francisco J. Aragón Artacho, Yair Censor, Aviv Gibali
The Douglas-Rachford (DR) algorithm is an iterative procedure that uses sequential reflections onto convex sets and which has become popular for convex feasibility problems. In thi…
- Regularization of Split Feasibility Problems
Abdellatif Moudafi, Aviv Gibali
Numerous problems in signal processing and imaging, statistical learning and data mining, or computer vision can be formulated as optimization problems which consist in minimizing…
Bounded perturbation resilience of extragradient-type methods and their applications
Qiao-Li Dong, Aviv Gibali, Dan Jiang +1
In this paper we study the bounded perturbation resilience of the extragradient and the subgradient extragradient methods for solving variational inequality (VI) problem in real Hi…
Convergence of projection and contraction algorithms with outer perturbations and their applications to sparse signals recovery
Qiao-Li Dong, Aviv Gibali, Dan Jiang +1
In this paper we study the bounded perturbation resilience of projection and contraction algorithms for solving variational inequality (VI) problems in real Hilbert spaces. Under t…
Physically Feasible Decomposition of Engino Toy Models: A Graph Theoretic Approach
Efstathios N. Antoniou, Adérito Araújo, Miguel D. Bustamante +1
During the 125th European Study Group with Industry held in Limassol, Cyprus, 5-9 December 2016, one of the participating companies, Engino.net Ltd, posed a very interesting challe…
Outer Approximation Methods for Solving Variational Inequalities in Hilbert Space
Aviv Gibali, Simeon Reich, Rafal Zalas
In this paper we study variational inequalities in a real Hilbert space, which are governed by a strongly monotone and Lipschitz continuous operator over a closed and convex se…
Speedup of lexicographic optimization by superiorization and its applications to cancer radiotherapy treatment
Esther Bonacker, Aviv Gibali, Karl-Heinz Küfer +1
Multicriteria optimization problems occur in many real life applications, for example in cancer radiotherapy treatment and in particular in intensity modulated radiation therapy (I…
The Implicit Convex Feasibility Problem and Its Application to Adaptive Image Denoising
Yair Censor, Aviv Gibali, Frank Lenzen +1
The implicit convex feasibility problem attempts to find a point in the intersection of a finite family of convex sets, some of which are not explicitly determined but may vary. We…
An algorithm for solving the variational inequality problem over the fixed point set of a quasi-nonexpansive operator in Euclidean space
Andrzej Cegielski, Aviv Gibali, Simeon Reich +1
This paper is concerned with the variational inequality problem (VIP) over the fixed point set of a quasi-nonexpansive operator. We propose, in particular, an algorithm which entai…