-
ProxToolbox, D. R. Luke. A toolbox of algorithms and projection
operators for implementing fixed point iterations based on the
Prox operator.
(2012).
-
Symbolic Convex Analysis Toolkit (SCAT) C. Hamilton et al.
The Symbolic Convex Analysis Toolkit (SCAT) is a Maple package for
symbolic computation of various objects from convex anlysis
including Fenchel conjugates and subdifferentials. We are actively
working on further development of the package but the bulk of the
source code is credited to Borwein & Hamilton. The archive also
contains supplementary material for the paper
Symbolic computation
with monotone operators (2017)
-
Samsara is a reverse communication nonlinear optimization solver for smooth
unconstrained objectives. The library functions as an oracle that suggests a step
(direction and length) using previous information provided to it by the calling routine.
It does not execute function evaluations or gradient calculations, but it does build a model
of the function being optimized, based on the steps, gradients and function values
(if available) passed to it by the user. Fortran, Matlab, and Python implementations
are available in the
compressed-tar-file.
Books
-
Nanoscale Photonic Imaging, T. Salditt, A. Egner, and D.R. Luke (eds). Springer Cham. (2020).
-
Splitting Algorithms, Monotone Operators Theory and Applications, H. Bauschke, R. Burachik, and D.R. Luke ed. Springer Verlag (2019).
-
Fixed-Point Algorithms for Inverse Problems in Science and Engineering, H. Bauschke, R. Burachik, P. Combettes, V. Elser, R. Luke, H. Wolkowicz, ed. Springer Verlag (2011).
-
Experimental Mathematics in Action, with David Bailey,
Jonathan Borwein, Neil Calkin, Roland Girgensohn, and Victor Moll. A. K. Peters (2007).
Refereed Journal Publications/Refereed Chapters
- ``A Semi-Bregman Proximal Alternating Method for a Class of Nonconvex Problems: Local and Global Convergence Analysis ",
E. Cohen, D. R. Luke, T. Pinta, S. Sabach and M. Teboulle. J. Global Optimization, (2023).
- ``Nonexpansive Markov Operators and Random Function Iterations for Stochastic Fixed Point Problems ",
N. Hermer, D. R. Luke and A. Sturm. J. Convex Analysis, (2023)
30:4, 1073--1114.
arXiv preprint
- `` Formation of moiré interlayer excitons in space and time",
D. Schmitt, J. P. Bange, W. Bennecke, A.A. AlMutairi, G. Meneghini, K. Watanabe,
T. Taniguchi, D. Steil, D. R. Luke, R. T. Weitz, S. Steil, G. S. M. Jansen,
S. Brem, E. Malic, S. Hofmann, M. Reutzel and S. Mathias Nature
608, 499--503 (2022).
DOI 10.1038/s41586-022-04977-7
- `` α-firmly Nonexapansive Operators on Metric Spaces",
A. Berdellima, F. Lauster and D. R. Luke. J. Fixed Point Theory and Applications(2022)
24:14.
DOI 10.1007/s11784-021-00919-4
- ``Projection methods for high numerical aperture
phase retrieval
",
H. N. Thao, O. Soloviev, D. R. Luke and M. Verhaegen. Inverse Problems 37(2021) 125005.
DOI 10.1088/1361-6420/ac3322
- `` Convergence of proximal splitting algorithms in CAT(k) spaces and beyond ",
F. Lauster and D. R. Luke. Fixed Point Theory Algorithms Sci Eng 2021, 13 (2021).
DOI 10.1186/s13663-021-00698-0
- ``Efficient orbital imaging based on ultrafast momentum microscopy and sparsity-driven phase retrieval",
G. S. M. Jansen, M. Keunecke, M. Duevel, C. Moeller, D. Schmitt, W. Bennecke, F. J. S. Kappert, D. Steil, D. R. Luke, S. Steil, S. Mathias. New Journal of Physics, 22 063012 (2020).
- ``Phase retrieval with sparse phase constraint",
H. N. Thao, D. R. Luke, O. Soloviev, M. Verhaegen. SIAM J. Mathematics of Data Science, 2(1):246-263 (2020).
- ``Convergence Analysis of the Relaxed Douglas Rachford Algorithm" ,
D. R. Luke and A.-L. Martins , SIAM J. on Optimization, 30(1):542--584(2020).
-
``
Necessary conditions for linear convergence of iterated
expansive, set-valued mappings
'', D. R. Luke M. Teboulle and N.H Thao, Mathematical Programming A 180(1), 1-31 (2020).
DOI:10.1007/s10107-018-1343-8 .
- `` Optimization on Spheres: Models and Proximal
Algorithms with Computational Performance Comparisons" ,
D. R. Luke, S. Sabach and M. Teboulle , SIAM J. Mathematics of Data Science, 1(3), 408-445 (2019).
Accompanying code.
Stored separately: data.
- ``
Characterizations of Super-regularity and its Variants"
,
A. Daniilidis, D. R. Luke and M. K. Tam , in
Splitting Algorithms, Modern Operator Theory and Applications,
H. H. Bauschke, D. R. Luke and R. Burachik eds. Springer, (2019).
DOI:10.1007/978-3-030-25939-6_6. ( arXiv)
- ``
Tangent and Normal Cones for Low-Rank Matrices" , S. Hosseini, D. R. Luke and A. Uschmajew, in
Nonsmooth Optimization and Its Applications,
S. Hosseini, B. S. Mordukhovich, and A.Uschmajew (Eds.),
Birkhauser, (2019). DOI: 10.1007/978-3-030-11370-4_3. (preprint)
-
`` Random Function Iterations for Consistent Stochastic Feasibility
'', N. Hermer, D.R. Luke and A. Sturm, Numerical Functional Analysis and Optimization 40(4):386--420 (2019).
DOI: 10.1080/01630563.2018.1535507.
-
``
Quantitative convergence analysis of iterated expansive,
set-valued mappings
'', D. R. Luke, and N. H. Thao and M. K. Tam, Mathematics
of Operations Research 43(4):1143--1176 (2018).
DOI https://doi.org/10.1287/moor.2017.0898.
-
``Block-coordinate primal-dual method for nonsmooth minimization over linear constraints
'',
D. R. Luke and Y. Malitsky,
Distributed and Large-Scale Optimization
P. Giselsson and A. Rantzer ed. Springer, 2018. DOI https://doi.org/10.1007/978-3-319-97478-1_6
-
``
Symbolic Computation with Monotone Operators
'', F. Lauster, D. R. Luke and M. K. Tam,
J. Set Valued and Variational Analysis, (2018) 26:353--368,
DOI 10.1007/s11228-017-0418-7
(arXiv:1703.05946). Accompanying
code.
-
``
Implicit Error Bounds for Picard Iterations on Hilbert
Spaces
'', D. R. Luke, and N. H. Thao. and M. K. Tam, Vietnam J. Mathematics, 46(2), 243-258 (2018).
DOI: 10.1007/s10013-018-0279-x
-
``Set Regularities and Feasibility
Problems
'', A. Y. Kruger, D. R. Luke, and N. H. Thao,
Mathematical Programming B, (2018) 168: 279--311.
DOI 10.1007/s10107-016-1039-x
-
``A Globally Linearly Convergent Method for Pointwise Quadratically Supportable Convex-Concave Saddle Point Problems'',
D. R. Luke and R. Shefi, J. Math. Anal. and Appl. 457(2), 1568--1590 (2018). DOI 10.1016/j.jmaa.2017.02.068
-
``About Subtransversality of Collections of Sets
'', A. Y. Kruger, D. R. Luke, and N. H. Thao,
Set-Valued and Variational Analysis, 25(4), 701-729 (2017).
DOI 10.1007/s11228-017-0436-5
-
``
A Simple Globally Convergent Algorithm for the Nonsmooth Nonconvex Single Source Localization Problems
'', D. R. Luke, S. Sabach, M. Teboulle, and K. Zatlawey.
J. Global Optimization (2017) 69: 889--909.
DOI 10.1007/s10898-017-0545-6
-
``
Lagrange Multipliers, (Exact) Regularization and Error Bounds for
Monotone Variational Inequalities
'', C. Charitha, J. Dutta and D. R. Luke,
Mathematical Programming A(2017) 161: 519--549.
DOI 10.1007/s10107-016-1022-6
-
``
Local Linear Convergence of the ADMM/Douglas--Rachford Algorithms without Strong Convexity
and Application to Statistical Imaging
'', T. Aspelmeier, C. Charitha and D. R. Luke,
SIAM J. Imaging Sciences 9(2):842-868 (2016). DOI https://doi.org/10.1137/15M103580X.
-
``Proximal Heterogeneous Block Implicit-Explicit Method and Application to Blind Ptychographic Diffraction Imaging
'', R. Hesse, D. R. Luke, S. Sabach and M. K. Tam,
SIAM J. on Imaging Sciences, 8(1):426--457 (2015).
DOI https://doi.org/10.1137/14098168X
-
``Alternating Projections and Douglas-Rachford for Sparse Affine Feasibility
'', R. Hesse, D. R. Luke and P. Neumann
IEEE Transactions on Signal Processing, 62(18):4868--4881, 2014.
DOI 10.1109/TSP.2014.2339801
-
``Reconstruction of wave front and object for inline holography from a set of detection planes
'', J. Hagemann, A.-L. Robisch, D. R. Luke, C. Homann, T. Hohage, P. Cloetens, H. Suhonen and T. Salditt,
Optics Express 22(2014): 11552-11569.
DOI https://doi.org/10.1364/OE.22.011552
-
``Restricted normal cones and
sparsity optimization with affine contraints.
'', H. H. Bauschke, D. R. Luke, H. M. Phan and X. Wang,
Foundations of Computational Mathematics 14(1):63--83 (2014).
DOI 10.1007/s10208-013-9161-0
-
``Restricted normal cones and the
method of alternating projections: applications
'', H. H. Bauschke, D. R. Luke, H. M. Phan, and X. Wang,
J. Set-Valued and Variational Analysis 21:475--501
(2013) DOI 10.1007/s11228-013-0238-3.
-
``Restricted normal cones and the
method of alternating projections: theory
'', H. H. Bauschke, D. R. Luke, H. M. Phan and X. Wang,
J. Set-Valued and Variational Analysis 21:431--473
(2013) DOI 10.1007/s11228-013-0239-2.
-
``
Nonconvex notions of regularity and convergence of fundamental
algorithms for feasibility problems
'', R. Hesse and D. R. Luke, SIAM J. Optim. 23(4), 2397-2419, 2013.
DOI https://doi.org/10.1137/120902653.
-
``Prox-regularity of rank constraint sets and implications for algorithms
'', D. R. Luke,
J. Math. Imaging and Vision, 47(3):231--328 (2013).
DOI: 10.1007/s10851-012-0406-3
-
``Local Linear Convergence of Approximate Projections onto Regularized Sets
'', D. R. Luke,
Nonlinear Analysis, 75(2012):1531--1546.
DOI: 10.1016/j.na.2011.08.027.
(preprint: arXiv:1108.2243v3)
- ``
Entropic Regularization of the l_0 Function
'', J. M. Borwein and D. R. Luke, in
Fixed-Point Algorithms for Inverse Problems in Science and Engineering,
H. Bauschke, R. Burachik, P. Combettes, V. Elser, R. Luke, H. Wolkowicz, ed. Springer Verlag (2011). (Preprint)
-
``Duality and Convex Programming
'', J. M. Borwein and D. R. Luke, pp. 257--304 (2015).
In Scherzer O.(eds), Handbook of Mathematical Methods in Imaging. Springer, New York, NY.
DOI https://doi.org/10.1007/978-1-4939-0790-8_7
-
`` MUSIC for Extended Scatterers as an Instance of the
Factorization Method
'', T. Arens, A. Lechleiter and D. R. Luke,
SIAM J. Appl. Math.70(4):1284-1304 (2009).
DOI https://doi.org/10.1137/080737836
-
`` Local convergence for alternating and averaged
nonconvex projections
'', A. S. Lewis, D. R. Luke and J. Malick,
Foundations of Computational Mathematics 9(4):485--513 (2009). DOI https://doi.org/10.1007/s10208-008-9036-y
-
`` Robust Mixing for Ab-Initio Quantum Mechanical Calculations'' L.D. Marks and D. R. Luke,
Phys. Rev. B 78:075114(2008).
DOI https://doi.org/10.1103/PhysRevB.78.075114
-
`` Finding best approximation pairs relative to a convex and a prox-regular set in a Hilbert space
'',
SIAM J. Opt. 19(2): 714--739 (2008). DOI https://doi.org/10.1137/070681399
-
`` Identifying scattering obstacles by the
construction of nonscattering waves'', with Tony Devaney.
SIAM J. Appl. Math. 68:271--291(2007). DOI https://doi.org/10.1137/060674430
-
`` The Point Source Method for Inverse
Scattering in the Time Domain'', with Roland Potthast.
Mathematical Methods in the Applied Sciences 29(3):
1501--1521(2006). DOI https://doi.org/10.1002/mma.738
-
`` A Strongly Convergent Reflection Method for Finding the Projection
onto the Intersection of Two Closed Convex Sets in a Hilbert Space"
with H. H. Bauschke and P. L. Combettes, Journal of Approximation Theory 141(1):63-69 (2006).
-
`` Dynamics of a Ramanujan-type Continued Fraction with
Cyclic Coefficients"
with Jonathan Borwein, The Ramanujan Journal16:285--304 (2008).
-
`` Dynamics of a Continued
Fraction of Ramanujan with Random Coefficients"
with Jonathan Borwein. Abstract and Applied Analysis 2005(5):449--467(2005).
-
`` Relaxed Averaged
Alternating Reflections for Diffraction Imaging", Inverse
Problems 21:37-50(2005).
- `` Image synthesis for inverse obstacle scattering using
the eigenfunction expansion theorem", Computing 75(2-3):181-196(2005).
- `` Finding
Best Approximation Pairs Relative to Two Closed Convex Sets in Hilbert
Spaces", with H. Bauschke and P. Combettes,
Journal of Approximation Theory 127:178-192(2004).
- `` Multifrequency
inverse obstacle scattering: the point source method and generalized
filtered backprojection" Mathematics and Computers in Simulation
66:297-314(2004). DOI https://doi.org/10.1016/j.matcom.2004.02.009
- `` Variational
analysis applied to the problem of optical phase retrieval", J. V. Burke
and D.R. Luke. SIAM J. Control Opt. 42(2):576-595
(2003). DOI https://doi.org/10.1137/S0363012902406436
-
`` A Hybrid
Projection Reflection Method for Phase Retrieval", H. H. Bauschke, P.
L. Combettes, and D. R. Luke. J. Opt. Soc. Am. A , 20(6):1025-1034
(2003).
-
`` The
no response test - a sampling method for inverse scattering problems ",
D. R. Luke and R. Potthast.
SIAM J. App. Math. , 63(4):1292-1312 (2003). DOI https://doi.org/10.1137/S0036139902406887
-
`` Phase
retrieval,
error reduction algorithm, and Fienup variants: A view from convex
optimization'',
H. H. Bauschke, P.
L. Combettes, and D. R. Luke.
J. Opt. Soc. Am. A, 19(7):1334-1345 (2002).
-
`` Optical
Wavefront
Reconstruction: Theory and Numerical Methods'', D. R.
Luke,
J. V.
Burke
and R. G. Lyon. SIAM
Review 44:169-224 (2002). DOI https://doi.org/10.1137/S003614450139075
Refereed
Conference
Proceedings
-
``Relaxed Cyclic Douglas-Rachford Algorithms for Nonconvex Optimization
'', D. R. Luke, A. Martins and M. K. Tam.
ICML 2018 Workshop: Modern Trends in Nonconvex Optimization for Machine Learning, Stockholm, July 2018.
-
``
Activity Identification and Local Linear
Convergence of Douglas-Rachford/ADMM
under Partial Smoothness
'',
J. Liang, J. Fadili, G. Peyre and D. R. Luke
Conference on
Scale Space and Variational Methods in Computer Vision
(2015)
-
``
PROJECTION METHODS FOR SPARSE AFFINE FEASIBILITY:
RESULTS AND COUNTEREXAMPLES
'',
H. Hesse, D. R. Luke and P. Neumann.
Signal Processing with Adaptive Sparse Structured Representations
,
(Lausanne, 2013).
-
``A New Generation of Iterative Transform
Algorithms for Phase Contrast Tomography'',
D. R. Luke, H. H. Bauschke and P. L. Combettes. Proceedings
of the IEEE 2005 International
Conference on Acoustics, Speech and Signal Processing,
(Philadelphia, PA, 2005).
-
`` On the
structure of Some Phase Retrieval Algorithms'', H. H. Bauschke, P.
C. Combettes, and D. R. Luke. Proceedings of the IEEE
International Conference
on Image Processing, vol II, pp. 841-844 (Rochester, NY,
September 22-25, 2002).
-
``The
Point Source Method in Acoustic Scattering : numerical
reconstruction
of the scattered field from far field measurements of inhomogeneous
media'',
D. R. Luke and R. Potthast. Proceedings of the IEEE 2002
International
Conference on Acoustics, Speech and Signal Processing,
pp.IV-3541-IV-3544 (Orlando, FL, May 13-17, 2002).
-
``Fast
Algorithms for Phase Retrieval and Deconvolution'', in Proceedings
of the Workshop on Computational Optics and Imaging for Space
Applications
pp.130-150 (NASA/Goddard Space Flight Center, May 10-12,
2000).
Invited
Articles and Reviews
- ``The proximal point algorithm without monotonicity", D. R. Luke and M. K. Tam.
Proceedings of the 35th RAMP Symposium,
Tokyo Institute of Technology, Tokyo, November 20-21, 2023.
-
D. R. Luke (2020) ``Proximal Methods for Image Processing
'', pp. 165-202. In: Salditt T., Egner, A. Luke, D.R. (eds)
Nanoscale Photonic Imaging,
Topics in Applied Physics, vol 134. Springer, Cham.
Accompanying codes,
phase data and
ptychography data.
-
D. R. Luke, C. Charitha, R. Shefi, and Y. Malitsky (2020) ``
Efficient, Quantitative Numerical Methods for Statistical Image Deconvolution and Denoising'',
pp. 313-338. In: Salditt T., Egner, A. Luke, D.R. (eds)
Nanoscale Photonic Imaging,
Topics in Applied Physics, vol 134. Springer, Cham.
-
D. R. Luke and A.-L. Martins (2020) ``
Convergence Analysis of Iterative Algorithms for Phase Retrieval'',
pp. 583-601. In: Salditt T., Egner, A. Luke, D.R. (eds)
Nanoscale Photonic Imaging,
Topics in Applied Physics, vol 134. Springer, Cham.
-
``Phase Retrieval. What's New?
'', D. R. Luke,
SIAG/OPT Views and News, 25(1):1--5 (2017).
-
``Duality and Convex Programming
'', J. M. Borwein and D. R. Luke, pp.257--304 (2015).
In Scherzer O.(eds), Handbook of Mathematical Methods in Imaging. Springer, New York, NY.
DOI https://doi.org/10.1007/978-1-4939-0790-8_7
- ``Calculus Without Derivatives'' a review of Jean-Paul Penot's
book in SIAM Review Book Reviews (2014).
- ``The Factorization Method for Inverse Problems'' a review of Andreas Kirsch and Natalia Grinberg's
book in SIAM Review Book Reviews 51(2):446-449 (2009).
- ``E Unibus Fissiparousness'' a review of David Foster
Wallace's Everything and More: A Compact History of Infinity in SIAM
Review Book Reviews, 47(1):178-182 (2005).
- `` A Simple Multiresolution Technique for Diffraction Image
Recovery," in the Pacific
Institute for the Mathematical Sciences Newsletter, 7(2):17-20
(2003).
Industry
Consulting
- ``Entfaltung von Laserspektren'', D. R. Luke and R.
Potthast. for Lambda Physik AG, September 2001.
- ``An Integration of Ellipsometry into Inverse Rough Surface
Scattering'', Klaus Erhard, D. Russell Luke and Roland Potthast.
for Nannofilm, GmBH, April 2002.
- ``Optimal switching of hybrid motors'',
IAV GmBH, October 2012-February 2013.
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