552 citations · 1.2k across the 33 of their papers we have counts for
33 papers
Rates of Convergence for Chains of Expansive Markov Operators
Neal Hermer, D. Russell Luke, Anja Sturm
We provide conditions that guarantee local rates of convergence in distribution of iterated random functions that are not nonexpansive mappings in locally compact Hadamard spaces.…
Nonexpansive Markov Operators and Random Function Iterations for Stochastic Fixed Point Problems
Neal Hermer, D. Russell Luke, Anja Sturm
We study the convergence of random function iterations for finding an invariant measure of the corresponding Markov operator. We call the problem of finding such an invariant measu…
Formation of moiré interlayer excitons in space and time
David Schmitt, Jan Philipp Bange, Wiebke Bennecke +11
Moiré superlattices in atomically thin van-der-Waals heterostructures hold great promise for an extended control of electronic and valleytronic lifetimes, the confinement of excito…
Convergence of Proximal Splitting Algorithms in CAT(k) Spaces and Beyond
Florian Lauster, D. Russell Luke
In the setting of CAT(k) spaces, common fixed point iterations built from prox mappings (e.g. prox-prox, Krasnoselsky-Mann relaxations, nonlinear projected-gradients) converge loca…
-Firmly Nonexpansive Operators on Metric Spaces
Arian Bërdëllima, Florian Lauster, D. Russell Luke
We extend to -uniformly convex spaces tools from the analysis of fixed point iterations in linear spaces. This study is restricted to an appropriate generalization of single-val…
Random Function Iterations for Stochastic Fixed Point Problems
Neal Hermer, D. Russell Luke, Anja Sturm
We study the convergence of random function iterations for finding an invariant measure of the corresponding Markov operator. We call the problem of finding such an invariant measu…
Efficient orbital imaging based on ultrafast momentum microscopy and sparsity-driven phase retrieval
G. S. M. Jansen, M. Keunecke, M. Düvel +8
We present energy-resolved photoelectron momentum maps for orbital tomography that have been collected with a novel and efficient time-of-flight momentum microscopy setup. This set…
Convergence Analysis of the Relaxed Douglas-Rachford Algorithm
D. Russell Luke, Anna-Lena Martins
Motivated by nonconvex, inconsistent feasibility problems in imaging, the relaxed alternating averaged reflections algorithm, or relaxed Douglas-Rachford algorithm (DR), was fir…
Optimization on Spheres: Models and Proximal Algorithms with Computational Performance Comparisons
D. Russell Luke, Shoham Sabach, Marc Teboulle
We present a unified treatment of the abstract problem of finding the best approximation between a cone and spheres in the image of affine transformations. Prominent instances of t…
Random Function Iterations for Consistent Stochastic Feasibility
Neal Hermer, D. Russell Luke, Anja Sturm
We study the convergence of stochastic fixed point iterations in the consistent case (in the sense of Butnariu and Flåm (1995)) in several different settings, under decreasingly re…
Characterizations of Super-regularity and its Variants
Aris Daniilidis, D. Russell Luke, Matthew K. Tam
Convergence of projection-based methods for nonconvex set feasibility problems has been established for sets with ever weaker regularity assumptions. What has not kept pace with th…
Phase retrieval with sparse phase constraint
Hieu Thao Nguyen, D. Russell Luke, Oleg Soloviev +1
For the first time, this paper investigates the phase retrieval problem with the assumption that the phase (of the complex signal) is sparse in contrast to the sparsity assumption…
Block-coordinate primal-dual method for the nonsmooth minimization over linear constraints
D. Russell Luke, Yura Malitsky
We consider the problem of minimizing a convex, separable, nonsmooth function subject to linear constraints. The numerical method we propose is a block-coordinate extension of the…
Necessary conditions for linear convergence of iterated expansive, set-valued mappings with application to alternating projections
D. Russell Luke, Marc Teboulle, Nguyen H. Thao
We present necessary conditions for monotonicity, in one form or another, of fixed point iterations of mappings that violate the usual nonexpansive property. We show that most reas…
Symbolic computation with monotone operators
Florian Lauster, D. Russell Luke, Matthew K. Tam
We consider a class of monotone operators which are appropriate for symbolic representation and manipulation within a computer algebra system. Various structural properties of the…
A Globally Linearly Convergent Method for Pointwise Quadratically Supportable Convex-Concave Saddle Point Problems
D. Russell Luke, Ron Shefi
We study the \emph{Proximal Alternating Predictor-Corrector} (PAPC) algorithm introduced recently by Drori, Sabach and Teboulle to solve nonsmooth structured convex-concave saddle…
About subtransversality of collections of sets
Alexander Y. Kruger, D. Russell Luke, Nguyen H. Thao
We provide dual sufficient conditions for subtransversality of collections of sets in an Asplund space setting. For the convex case, we formulate a necessary and sufficient dual cr…
Quantitative convergence analysis of iterated expansive, set-valued mappings
D. Russell Luke, Nguyen H. Thao, Matthew K. Tam
We develop a framework for quantitative convergence analysis of Picard iterations of expansive set-valued fixed point mappings. There are two key components of the analysis. The fi…
Set Regularities and Feasibility Problems
Alexander Y. Kruger, D. Russell Luke, Nguyen H. Thao
We synthesize and unify notions of regularity, both of individual sets and of collections of sets, as they appear in the convergence theory of projection methods for consistent fea…
Local Linear Convergence of the ADMM/Douglas--Rachford Algorithms without Strong Convexity and Application to Statistical Imaging
Timo Aspelmeier, C. Charitha, D. Russell Luke
We consider the problem of minimizing the sum of a convex function and a convex function composed with an injective linear mapping. For such problems, subject to a coercivity condi…
Activity Identification and Local Linear Convergence of Douglas--Rachford/ADMM under Partial Smoothness
Jingwei Liang, Jalal Fadili, Gabriel Peyré +1
Convex optimization has become ubiquitous in most quantitative disciplines of science, including variational image processing. Proximal splitting algorithms are becoming popular to…
Lagrange Multipliers, (Exact) Regularization and Error Bounds for Monotone Variational Inequalities
C. Charitha, Joydeep Dutta, D. Russell Luke
We examine two central regularization strategies for monotone variational inequalities, the first a direct regularization of the operative monotone mapping, and the second via regu…
Proximal Heterogeneous Block Input-Output Method and application to Blind Ptychographic Diffraction Imaging
Robert Hesse, D. Russell Luke, Shoham Sabach +1
We propose a general alternating minimization algorithm for nonconvex optimization problems with separable structure and nonconvex coupling between blocks of variables. To fix our…
Alternating Projections and Douglas-Rachford for Sparse Affine Feasibility
Robert Hesse, D. Russell Luke, Patrick Neumann
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 num…