Research

Preprints

  • A First-order algorithm for decentralised min-max problems
    with Y. Malitsky.
    arXiv:2308.11876, 2023.
    [arXiv]
  • Single-projection procedure for infinite dimensional convex optimization problems
    with H. T. Bui, R. S. Burachik and E. A. Nurminski.
    arXiv:2210.11252, 2022.
    [arXiv]
  • A Douglas—Rachford construction of non-separable continuous compactly supported multidimensional wavelets
    with D. Franklin and J. A. Hogan.
    arXiv:2006.03302, 2020.
    [arXiv]

Journal Publications

  1. Resolvent splitting for sums of monotone operators with minimal lifting
    with Y. Malitsky.
    Mathematical Programming, 201:231-262, 2023.
    [Link] [arXiv]
  1. Frugal and decentralised resolvent splittings defined by nonexpansive operators.
    Optimization Letters, 2023.
    [Link] [arXiv]
  1. Bregman Golden ratio algorithms for variational inequalities
    with D. J. Uteda.
    Journal of Optimization Theory and Applications, 2023.
    [Link] [arXiv]
  1. Method of alternating projection for the absolute value equation
    with J. H. Alcantara and J.-S. Chen.
    Journal of Fixed Point Theory and Applications, 25(39), 2022.
    [Link] [arXiv]
  1. Distributed forward-backward methods for ring networks
    with F. J. Aragón-Artacho, Y. Malitsky and D. Torregrosa-Belén.
    Computational Optimization and Applications, 2022.
    [Link] [arXiv]
  1. Strengthened splitting methods for computing resolvents
    with F. J. Aragón Artacho and R. Campoy.
    Computational Optimization and Applications, 80(2):549-585, 2021.
    [Link] [arXiv]
  1. Convergence rates for boundedly regular systems
    with E. R. Csetnek and A. Eberhard.
    Advances in Computational Mathematics, 47, 2021.
    [Link] [arXiv]
  1. Constraint reduction reformulations for projection algorithms with applications to wavelet construction
    with M. N. Dao, N. Dizon and J. A. Hogan.
    Journal of Optimization Theory and Applications, 190:201-232, 2021.
    [Link] [arXiv]
  1. Gearhart—Koshy acceleration for affine subspaces.
    Operations Research Letters, 49(2):157-163, 2021.
    [Link] [arXiv]
  1. The Douglas-Rachford algorithm for convex and nonconvex feasibility problems
    with F. J. Aragón Artacho and R. Campoy.
    Mathematical Methods of Operations Research, 91:201-240, 2020.
    [Link] [arXiv]
  1. A forward-backward splitting method for monotone inclusions without cocoercivity
    with Y. Malitsky.
    SIAM Journal on Optimization, 30(2):1451-1472, 2020.
    [Link] [arXiv]
  1. Backward-forward-reflected-backward splitting for three operator monotone inclusions
    with J. Rieger.
    Applied Mathematics and Computation, 381:125248, 2020.
    [Link] [arXiv]
  1. Shadow Douglas—Rachford splitting for monotone inclusions
    with E. R. Csetnek and Y. Malitsky.
    Applied Mathematics and Optimization, 80:665-678, 2019.
    [Link] [arXiv]
  1. A Lyapunov-type approach to convergence of the Douglas—Rachford algorithm
    with M. N. Dao.
    Journal of Global Optimization, 73(1):83-112, 2019.
    [Link] [arXiv]
  1. Union averaged operators with applications to proximal algorithms for min-convex functions
    with M. N. Dao.
    Journal of Optimization Theory and Applications, 181(1):61-94, 2019.
    [Link] [arXiv]
  1. A feasibility approach for constructing combinatorial designs of circulant type
    with F. J. Aragón Artacho, R. Campoy and I. Kotsireas.
    Journal of Combinatorial Optimization, 35(4):1061-1085, 2018.
    [Link] [arXiv]
  1. Symbolic computation with monotone operators
    with F. Lauster and D. R. Luke.
    Set-Valued and Variational Analysis, 26:353-368, 2018.
    [Link] [arXiv]
  1. Implicit error bounds for Picard iterations on Hilbert spaces
    with D. R. Luke and H. T. Nguyen.
    Vietnam Journal of Mathematics, 46(2):243-258, 2018.
    [Link]
  1. Quantitative convergence analysis of iterated expansive, set-valued mappings
    with D. R. Luke and H. T. Nguyen.
    Mathematics of Operations Research, 43(4):1051-1404, 2018.
    [Link] [arXiv]
  1. Algorithms based on unions of nonexpansive maps.
    Optimization Letters, 12(5):1017-1027, 2018.
    [Link] [arXiv]
  1. Convergence rate analysis for averaged fixed point iterations in common fixed point problems
    with J. M. Borwein and G. Li.
    SIAM Journal on Optimization, 27(1):1-33, 2017.
    [Link] [arXiv]
  1. Regularity properties of non-negative sparsity sets.
    Journal of Mathematical Analysis and Applications, 447(2):758-777, 2017.
    [Link] [arXiv]
  1. Global behavior of the Douglas—Rachford method for a nonconvex feasibility problem
    with F. J. Aragón Artacho and J. M. Borwein.
    Journal of Global Optimization, 65:1-19, 2015.
    [Link] [arXiv]
  1. Norm convergence of realistic projection and reflection methods
    with J. M. Borwein and B. Sims.
    Optimization, 64(1):161-178, 2015.
    [Link] [arXiv]
  1. The cyclic Douglas—Rachford method for inconsistent feasibility problems
    with J. M. Borwein.
    Journal of Nonlinear and Convex Analysis, 16(4):573-584, 2015.
    [arXiv]
  1. Proximal heterogeneous block implicit-explicit method and application to blind ptychographic diffraction imaging
    with R. Hesse, D. R. Luke and S. Sabach.
    SIAM Journal on Imaging Sciences, 8(1):426-457, 2015.
    [Link] [arXiv]
  1. Recent Results on Douglas—Rachford methods for combinatorial optimization problems
    with F. J. Aragón Artacho and J. M. Borwein.
    Journal of Optimization Theory and Applications, 163:1-30, 2014.
    [Link] [arXiv]
  1. Douglas—Rachford feasibility methods for matrix completion problems
    with F. J. Aragón Artacho and J. M. Borwein.
    The ANZIAM Journal, 55(4):299-326, 2014.
    [Link] [arXiv]
  1. A cyclic Douglas—Rachford iteration scheme
    with J. M. Borwein.
    Journal of Optimization Theory and Applications, 160(1):1-29, 2014.
    [Link] [arXiv]
  1. Recent Results on Douglas—Rachford methods
    with F. J. Aragón Artacho and J. M. Borwein.
    Serdica Mathematical Journal, 39:313-330, 2013.
    [Link]
  1. Double layer structure of ionic liquids at the Au (111) electrode interface: an atomic force microscopy investigation
    with R. Hayes, N. Borisenko, P. C. Howlett, F. Endres and R. Atkin.
    The Journal of Physical Chemistry C, 115(14):6855-6863, 2011.
    [Link]

Conference Proceedings and Book Chapters

  1. The proximal point algorithm without monotonicity
    with D. R. Luke.
    In Proceedings of the 35th RAMP Mathematical Optimization Symposium, pages 39-48, Research Association of Mathematical Programming, 2023.
    [Link]
  1. Concrush: Understanding fugitive dust production and potential emission at a recycled concrete manufacturing facility
    with B. Florio, F. Georgiou, O. D. Y. Huet, M. E. Roberts and D. Triadis.
    In Proceedings of the 2020 Mathematics and Statistics in Industry Study Group, MISG-2020, pages M1-M41, 2022.
    [Link]
  1. Characterizations of super-regularity and its variants
    with A. Daniilidis and D. R. Luke.
    In Splitting Algorithms, Modern Operator Theory and Applications, pages 137-152, Springer, 2019.
    [arXiv]
  1. Higher-dimensional wavelets and the Douglas—Rachford algorithm
    with D. Franklin and J. A. Hogan.
    In 13th International Conference on Sampling Theory and Applications (SampTA), 2019.
    [Link]
  1. Reflection methods for inverse problems with application to protein conformation determination
    with J. M. Borwein.
    In Generalized Nash Equilibrium Problems, Bilevel Programming and MPEC, pages 83-100, Springer Singapore, 2018.
    [Link] [arXiv]
  1. Relaxed cyclic Douglas-Rachford algorithms for nonconvex optimization
    with D. R. Luke and A.-L. Martins.
    In ICML 2018: Workshop: Modern Trends in Nonconvex Optimization for Machine Learning, 2018.
    [Link]
  1. Improved stockyard management strategies for coal export terminals at Newcastle
    with N. Boland, D. Gulczynski, M. P. Jackson, M. W. P. Savelsbergh and M. K. Tam.
    In Proceedings of the 19th International Congress on Modelling and Simulation, pages 718-724, 2011.
    [Link]

Selected Talks

  1. Resolvent splitting with minimal lifting,
    One World Optimization Seminar, November 2021.
    [Video]

  2. How to Train a GAN,
    University Maths Olympics, October 2021.
    [Video]

  3. Gearhart-Koshy acceleration for affine subspaces,
    WoMBaT (online edition), December 2020.
    [Video]

  4. Splitting algorithms with forward steps,
    ICCOPT Berlin, August 2019.
    [PDF]

  5. Algorithms based on unions of nonexpansive maps,
    ISMP Boreduax, July 2018.
    [PDF]

  6. Symbolic convex analysis,
    CARMA Seminar at U. Newcastle, May 2017.
    [PDF]

  7. Algorithms for blind ptychographic imaging,
    CARMA Workshop on Mathematics and Computation at U. Newcastle, June 2015.
    [PDF]

  8. Theory and application of convex and non-convex feasibility problems
    Lecture Series (on behalf of J. Borwein), Spring School on Variational Analysis in Paseky nad Jizerou, Czech Republic, April 2015.
    [PDF] [URL]

  9. Reflection methods for Euclidean distance matrix reconstruction,
    Australian - New Zealand Mathematics Convention, Dec 2014.
    [PDF] [Video]

  10. Visualizing projection algorithms,
    ICERM Challenges in 21st Century Experimental Mathematical Computation Workshop, July 2014.
    [PDF] [Video]

  11. Cyclic Douglas-Rachford iterations,
    AustMS Annual Meeting, Sept-Oct 2013.
    [PDF]

  12. Douglas-Rachford for combinatorial optimisation,
    AMSSC, July 2013.
    [PDF]