21 citations · 44 across the 40 of their papers we have counts for
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Strong Convergence of FISTA for Affinely Constrained Convex Quadratic Minimization
Sedi Bartz, Heinz H. Bauschke, Yuan Gao +1
In October 2025, research by Boţ, Fadili, and Nguyen, and by Jang and Ryu, led to the seminal result that Beck and Teboulle's FISTA converges weakly to a minimizer of the sum of tw…
Understanding FISTA's weak convergence: A step-by-step introduction to the 2025 milestone
Heinz H. Bauschke, Walaa M. Moursi
Beck and Teboulle's FISTA for finding the minimizer of the sum of two convex functions is one of the most important algorithms of the past decades. While function value convergence…
Best Approximation Optimal Control for Infeasible Double Integrator and Douglas--Rachford Algorithm
Regina S. Burachik, Bethany I. Caldwell, C. Yalçın Kaya +1
We consider the problem of finding (in some sense) the best approximation control for an infeasible double integrator. The control function is constrained by upper and lower bounds…
Accelerated Proximal Gradient Methods in the affine-quadratic case: Strong convergence and limit identification
Walaa M. Moursi, Andrew Naguib, Viktor Pavlovic +1
Recent works by Bot-Fadili-Nguyen (arXiv:2510.22715) and by Jang-Ryu (arXiv:2510.23513) resolve long-standing iterate convergence questions for accelerated (proximal) gradient meth…
A necessary condition for the guarantee of the superiorization method
Kay Barshad, Yair Censor, Walaa Moursi +2
We study a method that involves principally convex feasibility-seeking and makes secondary efforts of objective function value reduction. This is the well-known superiorization met…
Eckstein-Ferris-Pennanen-Robinson duality revisited: paramonotonicity, total Fenchel-Rockafellar duality, and the Chambolle-Pock operator
Heinz H. Bauschke, Walaa M. Moursi, Shambhavi Singh
Finding zeros of the sum of two maximally monotone operators involving a continuous linear operator is a central problem in optimization and monotone operator theory. We revisit th…
Infeasible and Critically Feasible Optimal Control
Regina S. Burachik, C. Yalçın Kaya, Walaa M. Moursi
We consider optimal control problems involving two constraint sets: one comprised of linear ordinary differential equations with the initial and terminal states specified and the o…
Exact Solutions for the NP-hard Wasserstein Barycenter Problem using a Doubly Nonnegative Relaxation and a Splitting Method
Woosuk L. Jung, Henry Wolkowicz
The so-called \emph{simplified} Wasserstein barycenter problem, also known as the cheapest hub problem, consists in selecting one point from each of given sets, each set consis…
Accelerated gradient descent: A guaranteed bound for a heuristic restart strategy
Walaa M. Moursi, Viktor Pavlovic, Stephen A. Vavasis
The convergence rate in function value of accelerated gradient descent is optimal, but there are many modifications that have been used to speed up convergence in practi…
Range of the displacement operator of PDHG with applications to quadratic and conic programming
Tao Jiang, Walaa M. Moursi, Stephen A. Vavasis
Primal-dual hybrid gradient (PDHG) is a first-order method for saddle-point problems and convex programming introduced by Chambolle and Pock. Recently, Applegate et al.\ analyzed t…
On the Bredies-Chenchene-Lorenz-Naldi algorithm
Heinz H. Bauschke, Walaa M. Moursi, Shambhavi Singh +1
Monotone inclusion problems occur in many areas of optimization and variational analysis. Splitting methods, which utilize resolvents or proximal mappings of the underlying operato…
How averaged is the composition of two linear projections?
Heinz H. Bauschke, Theo Bendit, Walaa M. Moursi
Projection operators are fundamental algorithmic operators in Analysis and Optimization. It is well known that these operators are firmly nonexpansive; however, their composition i…
Optimal Control Duality and the Douglas-Rachford Algorithm
Regina S. Burachik, Bethany I Caldwell, C. Yalçın Kaya +1
We explore the relationship between the dual of a weighted minimum-energy control problem, a special case of linear-quadratic optimal control problems, and the Douglas-Rachford (DR…
Regularized Nonsmooth Newton Algorithms for Best Approximation
Yair Censor, Walaa M. Moursi, Tyler Weames +1
We consider the problem of finding the best approximation point from a polyhedral set, and its applications, in particular to solving large-scale linear programs. The classical pro…
How to project onto the intersection of a closed affine subspace and a hyperplane
Heinz H. Bauschke, Dayou Mao, Walaa M. Moursi
Let be a closed affine subspace and let be a hyperplane in a Hilbert space. Suppose we are given their associated nearest point mappings and , respectively. We p…
The range of the Douglas-Rachford operator in infinite-dimensional Hilbert spaces
Walaa M. Moursi
The Douglas-Rachford algorithm is one of the most prominent splitting algorithms for solving convex optimization problems. Recently, the method has been successful in finding a gen…
Strongly nonexpansive mappings revisited: uniform monotonicity and operator splitting
Leon Liu, Walaa M. Moursi, Jon Vanderwerff
The correspondence between the class of nonexpansive mappings and the class of maximally monotone operators via the reflected resolvents of the latter has played an instrumental ro…
On the Douglas-Rachford and Peaceman-Rachford algorithms in the presence of uniform monotonicity and the absence of minimizers
Regina S. Burachik, Bethany I. Caldwell, C. Yalçın Kaya +2
The Douglas-Rachford and Peaceman-Rachford algorithms have been successfully employed to solve convex optimization problems, or more generally find zeros of monotone inclusions. Re…
On the Douglas-Rachford algorithm for solving possibly inconsistent optimization problems
Heinz H. Bauschke, Walaa M. Moursi
More than 40 years ago, Lions and Mercier introduced in a seminal paper the Douglas-Rachford algorithm. Today, this method is well recognized as a classical and highly successful s…
On compositions of special cases of Lipschitz continuous operators
Pontus Giselsson, Walaa M. Moursi
Many iterative optimization algorithms involve compositions of special cases of Lipschitz continuous operators, namely firmly nonexpansive, averaged and nonexpansive operators. The…
On the behaviour of the Douglas-Rachford algorithm for minimizing a convex function subject to a linear constraint
Heinz H. Bauschke, Walaa M. Moursi
The Douglas-Rachford algorithm (DRA) is a powerful optimization method for minimizing the sum of two convex (not necessarily smooth) functions. The vast majority of previous resear…
Differentiating Through a Cone Program
Akshay Agrawal, Shane Barratt, Stephen Boyd +2
We consider the problem of efficiently computing the derivative of the solution map of a convex cone program, when it exists. We do this by implicitly differentiating the residual…
Generalized monotone operators and their averaged resolvents
Heinz H. Bauschke, Walaa M. Moursi, Xianfu Wang
The correspondence between the monotonicity of a (possibly) set-valued operator and the firm nonexpansiveness of its resolvent is a key ingredient in the convergence analysis of ma…
Numerical explorations of feasibility algorithms for finding points in the intersection of finite sets
Heinz H. Bauschke, Sylvain Gretchko, Walaa M. Moursi
Projection methods are popular algorithms for iteratively solving feasibility problems in Euclidean or even Hilbert spaces. They employ (selections of) nearest point mappings to ge…