Prof. Dr. David Russell Luke

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  • 2024 | Preprint
    ​ ​Stochastic Algorithms for Large-Scale Composite Optimization: the Case of Single-Shot X-FEL Imaging​
    Luke, D. R. ; Schultze, S.& Grubmüller, H. ​ (2024)
    ​Details 
  • 2023 | Conference Paper | 
    ​ ​The proximal point algorithm without monotonicity​
    Luke, D. R.   & Tam, M. K.​ (2023)
    In:Liu, Tianxiang; Yamashita, Makoto​ (Eds.), ​Proceedings of the 35th RAMP Mathematical Optimization Symposium pp. 39​-48. ​35th RAMP Mathematical Optimization Symposium​, Tokyo.
    Tokyo​: Research Association of Mathematical Programming.
    ​Details 
  • 2023 | Monograph | Textbook, Manual | 
    ​ ​Variational Numerical Analysis​ ​
    Luke, D. R. ​ (2023)
    ​Details 
  • 2023 | Journal Article
    ​ ​Nonexpansive Markov Operators and Random Function Iterations for Stochastic Fixed Point Problems: ​Random Function Iterations for Stochastic Fixed Point Problems​
    Hermer, N.; Luke, D. R.   & Sturm, A.​ (2023) 
    Journal of Convex Analysis, 30(4) pp. 1073​-1114​.​
    ​Details  WoS  arXiv 
  • 2023 | Preprint | 
    ​ ​Convergence in Distribution of Randomized Algorithms: The Case of Partially Separable Optimization​
    Luke, R.  & Luke, D. R. ​ (2023)
    ​Details  arXiv 
  • 2023 | Journal Article | Research Paper
    ​ ​A Semi-Bregman Proximal Alternating Method for a Class of Nonconvex Problems: Local and Global Convergence Analysis: ​Semi-Bregman Proximal Alternating Method​
    Cohen, E.; Pinta, T.; Sabach, S.; Teboulle, M. & Luke, D. R. ​ (2023) 
    Journal of Global Optimization,.​ DOI: https://doi.org/10.1007/s10898-023-01334-4 
    ​Details  DOI 
  • 2023 | Journal Article | Research Paper | 
    ​ ​Rates of Convergence for Chains of Expansive Markov Operators: ​Expansive Markov Operators​
    Hermer, N.; Luke, D. R.   & Sturm, A.​ (2023) 
    Transactions of Mathematics and its Applications, 7(1) pp. 1​-31​.​ DOI: https://doi.org/10.1093/imatrm/tnad001 
    ​Details  DOI  arXiv 
  • 2022 | Software
    ​ ​Samsara​
    Luke, David Russell  (2022)
    ​Details 
  • 2022 | Journal Article | Research Paper | 
    ​ ​α -Firmly nonexpansive operators on metric spaces​
    Bërdëllima, A.; Lauster, F. & Luke, D. R. ​ (2022) 
    Journal of Fixed Point Theory and Applications, 24(1) art. 14​.​ DOI: https://doi.org/10.1007/s11784-021-00919-4 
    ​Details  DOI 
  • 2022 | Journal Article
    ​ ​Formation of moiré interlayer excitons in space and time​
    Schmitt, D.; Bange, J. P.; Bennecke, W.; AlMutairi, A.; Meneghini, G.; Watanabe, K. & Taniguchi, T. et al.​ (2022) 
    Nature, 608(7923) pp. 499​-503​.​ DOI: https://doi.org/10.1038/s41586-022-04977-7 
    ​Details  DOI 
  • 2021 | Preprint
    ​ ​α-Firmly Nonexpansive Operators on Metric Spaces​
    Bërdëllima, A.; Lauster, F.& Luke, D. R. ​ (2021)
    ​Details  arXiv 
  • 2021 | Journal Article | Research Paper | 
    ​ ​Projection methods for high numerical aperture phase retrieval​
    Hieu Thao, N.; Soloviev, O.; Luke, R.   & Verhaegen, M.​ (2021) 
    Inverse Problems, 37(12) pp. 125005​.​ DOI: https://doi.org/10.1088/1361-6420/ac3322 
    ​Details  DOI 
  • 2020 | Book Chapter
    ​ ​Constrained Reconstructions in X-ray Phase Contrast Imaging: Uniqueness, Stability and Algorithms​
    Maretzke, S.& Hohage, T. ​ (2020)
    In:​Salditt, Tim; Egner, Alexander; Luke, Russell​ (Eds.), Nanoscale Photonic Imaging pp. 377​-403.  DOI: https://doi.org/10.1007/978-3-030-34413-9_14 
    ​Details  DOI 
  • 2020 | Book Chapter
    ​ ​Proximal Methods for Image Processing​
    Luke, D. R. ​ (2020)
    In:​Salditt, Tim; Egner, Alexander; Luke, D. Russell​ (Eds.), Nanoscale Photonic Imaging pp. 165​-202.  DOI: https://doi.org/10.1007/978-3-030-34413-9_6 
    ​Details  DOI 
  • 2020 | Anthology
    ​ ​Nanoscale Photonic Imaging​ ​
    Salditt, T. ; Egner, A.  & Luke, D. R. ​ (Eds.) (2020)
    Cham: ​Springer. DOI: https://doi.org/10.1007/978-3-030-34413-9 
    ​Details  DOI 
  • 2020 | Book Chapter
    ​ ​Efficient, Quantitative Numerical Methods for Statistical Image Deconvolution and Denoising​
    Luke, D. R. ; Charitha, C.; Shefi, R.& Malitsky, Y.​ (2020)
    In:​Salditt, Tim; Egner, Alexander; Luke, D. Russell​ (Eds.), Nanoscale Photonic Imaging pp. 313​-338.  DOI: https://doi.org/10.1007/978-3-030-34413-9_12 
    ​Details  DOI 
  • 2020 | Book Chapter
    ​ ​Convergence Analysis of Iterative Algorithms for Phase Retrieval​
    Luke, D. R.  & Martins, A.-L.​ (2020)
    In:​Salditt, Tim; Egner, Alexander; Luke, D. Russell​ (Eds.), Nanoscale Photonic Imaging pp. 583​-601.  DOI: https://doi.org/10.1007/978-3-030-34413-9_23 
    ​Details  DOI 
  • 2020 | Journal Article
    ​ ​Phase Retrieval with Sparse Phase Constraint​
    Thao, N. H.; Luke, D. R. ; Soloviev, O. & Verhaegen, M.​ (2020) 
    SIAM Journal on Mathematics of Data Science, 2(1) pp. 246​-263​.​ DOI: https://doi.org/10.1137/19M1266800 
    ​Details  DOI 
  • 2020 | Journal Article
    ​ ​Necessary conditions for linear convergence of iterated expansive, set-valued mappings​
    Luke, D. R. ; Teboulle, M. & Thao, N. H. ​ (2020) 
    Mathematical Programming, 180(1-2) pp. 1​-31​.​ DOI: https://doi.org/10.1007/s10107-018-1343-8 
    ​Details  DOI 
  • 2020 | Journal Article
    ​ ​Convergence Analysis of the Relaxed Douglas-Rachford Algorithm​
    Luke, D. R.   & Martins, A.-L.​ (2020) 
    SIAM Journal on Optimization, 30(1) pp. 542​-584​.​ DOI: https://doi.org/10.1137/18M1229638 
    ​Details  DOI 
  • 2020 | Journal Article | Research Paper | 
    ​ ​Efficient orbital imaging based on ultrafast momentum microscopy and sparsity-driven phase retrieval​
    Mathias, S. ; Jansen, G. S. M. ; Keunecke, M.; Düvel, M.; Möller, C.; Schmitt, D. & Bennecke, W. et al.​ (2020) 
    New Journal of Physics, 22(6) pp. 063012​.​ DOI: https://doi.org/10.1088/1367-2630/ab8aae 
    ​Details  DOI 
  • 2019 | Book Chapter
    ​ ​Tangent and Normal Cones for Low-Rank Matrices​
    Hosseini, S.; Luke, D. R.  & Uschmajew, A.​ (2019)
    In:​Hosseini, S.; Mordukhovich, B. S.; Uschmajew, A.​ (Eds.), Nonsmooth Optimization and Its Applications pp. 45​-53. (Vol. 170). ​Birkhauser. DOI: https://doi.org/10.1007/978-3-030-11370-4_3 
    ​Details  DOI 
  • 2019 | Anthology
    ​ ​Splitting Algorithms, Modern Operator Theory, and Applications​ ​(1. ed.) 
    Bauschke, H. H.; Burachik, R. S.& Luke, D. R. ​ (Eds.) (2019)
    Cham: ​Springer.
    ​Details 
  • 2019 | Journal Article
    ​ ​Random Function Iterations for Consistent Stochastic Feasibility​
    Hermer, N.; Luke, D. R.   & Sturm, A. ​ (2019) 
    Numerical Functional Analysis and Optimization, 40(4) pp. 386​-420​.​ DOI: https://doi.org/10.1080/01630563.2018.1535507 
    ​Details  DOI 
  • 2019 | Journal Article
    ​ ​Optimization on Spheres: Models and Proximal Algorithms with Computational Performance Comparisons​
    Luke, D. R. ; Sabach, S. & Teboulle, M.​ (2019) 
    SIAM Journal on Mathematics of Data Science, 1(3) pp. 408​-445​.​ DOI: https://doi.org/10.1137/18M1193025 
    ​Details  DOI 
  • 2019 | Book Chapter
    ​ ​Characterizations of Super-regularity and its Variants​
    Daniilidis, A.; Luke, D. R.  & Tam, M.​ (2019)
    In:​Bauschke, Heinz; Luke, D. Russell; Burachik, Regina​ (Eds.), Splitting Algorithms, Modern Operator Theory and Applications pp. 137​-152. ​Springer. DOI: https://doi.org/10.1007/978-3-030-25939-6_6 
    ​Details  DOI 
  • 2018 | Conference Paper
    ​ ​Relaxed Cyclic Douglas-Rachford Algorithms for Nonconvex Optimization​
    Luke, D. R. ; Martins, A. & Tam, M. K.​ (2018)
    ​ICML 2018 Workshop: Modern Trends in Nonconvex Optimization for Machine Learning​, Stockholm, Sweden.
    ​Details 
  • 2018 | Book Chapter
    ​ ​Block-Coordinate Primal-Dual Method for Nonsmooth Minimization over Linear Constraints​
    Luke, D. R.  & Malitsky, Y.​ (2018)
    In: Distributed and Large-Scale Optimization pp. 121​-147. (Vol. 2227).  DOI: https://doi.org/10.1007/978-3-319-97478-1_6 
    ​Details  DOI  arXiv 
  • 2018 | Journal Article
    ​ ​Implicit Error Bounds for Picard Iterations on Hilbert Spaces​
    Luke, D. R. ; Thao, N. H.   & Tam, M. K. ​ (2018) 
    Vietnam Journal of Mathematics, 46(2) pp. 243​-258​.​ DOI: https://doi.org/10.1007/s10013-018-0279-x 
    ​Details  DOI 
  • 2018 | Journal Article
    ​ ​A globally linearly convergent method for pointwise quadratically supportable convex–concave saddle point problems​
    Luke, D. R.   & Shefi, R.​ (2018) 
    Journal of Mathematical Analysis and Applications, 457(2) pp. 1568​-1590​.​ DOI: https://doi.org/10.1016/j.jmaa.2017.02.068 
    ​Details  DOI 
  • 2018 | Journal Article
    ​ ​Set regularities and feasibility problems​
    Kruger, A. Y.; Luke, D. R.   & Thao, N. H. ​ (2018) 
    Mathematical Programming, 168 pp. 279​-311​.​ DOI: https://doi.org/10.1007/s10107-016-1039-x 
    ​Details  DOI 
  • 2018 | Journal Article
    ​ ​Symbolic Computation with Monotone Operators​
    Lauster, F.; Luke, D. R.   & Tam, M. K. ​ (2018) 
    Set-Valued and Variational Analysis, 26(2) pp. 353​-368​.​ DOI: https://doi.org/10.1007/s11228-017-0418-7 
    ​Details  DOI 
  • 2018 | Journal Article | 
    ​ ​Quantitative Convergence Analysis of Iterated Expansive, Set-Valued Mappings​
    Thao, N. H. ; Tam, M. K.   & Luke, R. ​ (2018) 
    Mathematics of Operations Research, 43(4) pp. 1143​-1176​.​ DOI: https://doi.org/10.1287/moor.2017.0898 
    ​Details  DOI  arXiv 
  • 2017 | Journal Article
    ​ ​About Subtransversality of Collections of Sets​
    Kruger, A. Y.; Luke, D. R.   & Thao, N. H. ​ (2017) 
    Set-Valued and Variational Analysis, 25(4) pp. 701​-729​.​ DOI: https://doi.org/10.1007/s11228-017-0436-5 
    ​Details  DOI 
  • 2017 | Software
    ​ ​Symbolic Convex Analysis Toolkit (SCAT)​
    Luke, David Russell; Hamilton, C.  (2017)
    ​Details 
  • 2017 | Journal Article
    ​ ​Phase Retrieval, What's New?​
    Luke, R. ​ (2017) 
    SIAG/OPT Views and News, 25.​
    ​Details 
  • 2017 | Journal Article
    ​ ​Lagrange multipliers, (exact) regularization and error bounds for monotone variational inequalities​
    Charitha, C. ; Dutta, J. & Luke, R. ​ (2017) 
    Mathematical Programming, 161(1-2) pp. 519​-549​.​ DOI: https://doi.org/10.1007/s10107-016-1022-6 
    ​Details  DOI 
  • 2017 | Journal Article
    ​ ​A simple globally convergent algorithm for the nonsmooth nonconvex single source localization problem​
    Luke, D. R. ; Sabach, S.; Teboulle, M. & Zatlawey, K.​ (2017) 
    Journal of Global Optimization, 69(4) pp. 889​-909​.​ DOI: https://doi.org/10.1007/s10898-017-0545-6 
    ​Details  DOI 
  • 2016 | Journal Article
    ​ ​Local Linear Convergence of the ADMM/Douglas - Rachford Algorithms without Strong Convexity and Application to Statistical Imaging​
    Aspelmeier, T. ; Charitha, C.   & Luke, R. ​ (2016) 
    SIAM Journal on Imaging Sciences, 9(2) pp. 842​-868​.​ DOI: https://doi.org/10.1137/15m103580x 
    ​Details  DOI 
  • 2015 | Journal Article
    ​ ​Proximal Heterogeneous Block Implicit-Explicit Method and Application to Blind Ptychographic Diffraction Imaging​
    Hesse, R.; Luke, R. ; Sabach, S. & Tam, M. K. ​ (2015) 
    SIAM Journal on Imaging Sciences, 8(1) pp. 426​-457​.​ DOI: https://doi.org/10.1137/14098168x 
    ​Details  DOI 
  • 2015 | Book Chapter
    ​ ​Activity Identification and Local Linear Convergence of Douglas–Rachford/ADMM under Partial Smoothness​
    Liang, J.; Fadili, J.; Peyré, G.& Luke, R. ​ (2015)
    In:​Aujol, J. F.; Nikolova, M.; Papadakis, N.​ (Eds.), Scale Space and Variational Methods in Computer Vision pp. 642​-653. (Vol. 9087). ​Cham: ​Springer. DOI: https://doi.org/10.1007/978-3-319-18461-6_51 
    ​Details  DOI 
  • 2015 | Book Chapter
    ​ ​Duality and Convex Programming​
    Borwein, J. M.& Luke, R. ​ (2015)
    In:​Scherzer, Otmar​ (Ed.), Handbook of Mathematical Methods in Imaging. 2. ed.. ​New York, NY: ​Springer. DOI: https://doi.org/10.1007/978-1-4939-0790-8_7 
    ​Details  DOI 
  • 2014 | Journal Article | Research Paper | 
    ​ ​Reconstruction of wave front and object for inline holography from a set of detection planes​
    Hagemann, J. ; Robisch, A.-L. ; Luke, D. R. ; Homann, C.; Hohage, T. ; Cloetens, P. & Suhonen, H. et al.​ (2014) 
    Optics Express, 22(10) pp. 11552​-11569​.​ DOI: https://doi.org/10.1364/OE.22.011552 
    ​Details  DOI  PMID  PMC  WoS 
  • 2014 | Journal Article
    ​ ​Alternating Projections and Douglas-Rachford for Sparse Affine Feasibility​
    Hesse, R.; Luke, R.   & Neumann, P.​ (2014) 
    IEEE Transactions on Signal Processing, 62(18) pp. 4868​-4881​.​ DOI: https://doi.org/10.1109/tsp.2014.2339801 
    ​Details  DOI 
  • 2014 | Journal Article
    ​ ​Restricted Normal Cones and Sparsity Optimization with Affine Constraints​
    Bauschke, H. H.; Luke, D. R. ; Phan, H. M. & Wang, X.​ (2014) 
    Foundations of Computational Mathematics, 14(1) pp. 63​-83​.​ DOI: https://doi.org/10.1007/s10208-013-9161-0 
    ​Details  DOI 
  • 2013 | Journal Article
    ​ ​Restricted Normal Cones and the Method of Alternating Projections: Applications​
    Bauschke, H. H.; Luke, R. ; Phan, H. M. & Wang, X.​ (2013) 
    Set-Valued and Variational Analysis, 21(3) pp. 475​-501​.​ DOI: https://doi.org/10.1007/s11228-013-0238-3 
    ​Details  DOI 
  • 2013 | Journal Article
    ​ ​Nonconvex Notions of Regularity and Convergence of Fundamental Algorithms for Feasibility Problems​
    Hesse, R. & Luke, R. ​ (2013) 
    SIAM Journal on Optimization, 23(4) pp. 2397​-2419​.​ DOI: https://doi.org/10.1137/120902653 
    ​Details  DOI 
  • 2013 | Journal Article
    ​ ​Restricted Normal Cones and the Method of Alternating Projections: Theory​
    Bauschke, H. H.; Luke, R. ; Phan, H. M. & Wang, X.​ (2013) 
    Set-Valued and Variational Analysis, 21(3) pp. 431​-473​.​ DOI: https://doi.org/10.1007/s11228-013-0239-2 
    ​Details  DOI 
  • 2012 | Software
    ​ ​ProxToolbox​
    Luke, David Russell  (2012)
    ​Details 
  • 2011 | Book Chapter
    ​ ​Entropic Regularization of the ℓ 0 Function​
    Borwein, J. M.& Luke, D. R. ​ (2011)
    In:​Bauschke, Heinz H.; Burachik, Regina S.; Combettes, Patrick L.; Elser, Veit; Luke, D. Russell; Wolkowicz, Henry​ (Eds.), Fixed-Point Algorithms for Inverse Problems in Science and Engineering pp. 65​-92. ​New York: ​Springer. DOI: https://doi.org/10.1007/978-1-4419-9569-8_5 
    ​Details  DOI 
  • 2002 | Journal Article
    ​ ​Phase retrieval, error reduction algorithm, and Fienup variants: a view from convex optimization​
    Bauschke, H. H.; Combettes, P. L. & Luke, D. R. ​ (2002) 
    Journal of the Optical Society of America A, 19(7) art. 1334​.​ DOI: https://doi.org/10.1364/josaa.19.001334 
    ​Details  DOI 

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