Matthew K. Tam

See my work


I am Junior Professor for Mathematical Optimisation in the Institute for Numerical and Applied Mathematics at the University of Göttingen and a member of the Continuous Optimisation, Variational Analysis and Inverse Problems workgroup.

I received a PhD from the University of Newcastle (Australia) under the supervision of Jonathan Borwein where I was a member of the Centre for Computer-assisted Research Mathematics and its Applications (CARMA). My thesis was titled "Iterative projection and reflection methods: theory and practice". After my PhD, I moved to the University of Göttingen where I was a post-doctoral researcher with D. Russell Luke supported initially by DFG-GK2088 and later by a fellowship from the Alexander von Humboldt Foundation.

Research keywords: continuous optimisation and its applications, monotone operator theory, variational and nonsmooth analysis, heuristics derived from continuous optimisation, symbolic computation


  1. The Douglas-Rachford algorithm for convex and nonconvex feasibility problems with F.J. Aragón Artacho & R. Campoy. 2019. [arXiv] [BibTex]
  2. Shadow Douglas-Rachford splitting for monotone inclusions with E.R. Csetnek & Y. Malitsky. Applied Mathematics and Optimization, pages 1-14, 2019. [Link] [arXiv] [BibTex]
  3. A forward-backward splitting method for monotone inclusions without cocoercivity with Y. Malitsky. 2018. [arXiv] [BibTex]
  4. Union averaged operators with applications to proximal algorithms for min-convex functions with M.N. Dao. Journal of Optimization Theory and Applications, 1(181):61-94, 2019. [Link] [arXiv] [BibTex]
  5. A feasibility approach for constructing combinatorial designs of circulant type with F.J. Aragón Artacho, R. Campoy & I. Kotsireas. Journal of Combinatorial Optimization, 35(4):1061-1085, 2018. [Link] [arXiv] [BibTex]
  6. Algorithms based on unions of nonexpansive maps. Optimization Letters, 12(5):1017-1027, 2018. [Link] [arXiv] [BibTex]
  7. 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] [BibTex]
  8. Implicit error bounds for Picard iterations on Hilbert spaces with D.R. Luke & Nguyen H.T. Vietnam Journal of Mathematics, 46(2):243-258, 2018. [Link] [BibTex]
  9. Symbolic computation with monotone operators with F. Lauster & D.R. Luke. Set-Valued and Variational Analysis, 26:353-368, 2018. [Link] [arXiv] [BibTex]
  10. Regularity properties of non-negative sparsity sets. Journal of Mathematical Analysis and Applications, 447(2):758-777, 2017. [Link] [arXiv] [BibTex]
  11. Quantitative convergence analysis of iterated expansive, set-valued mappings with D.R. Luke & Nguyen H.T. Mathematics of Operations Research, published online July 2018. [Link] [arXiv] [BibTex]
  12. Convergence rate analysis for averaged fixed point iterations in common fixed point problems with J.M. Borwein & G. Li. SIAM Journal on Optimization, 27(1):1-33, 2017. [Link] [arXiv] [BibTex]
  13. Global behavior of the Douglas-Rachford method for a nonconvex feasibility problem with F.J. Aragón Artacho & J.M. Borwein. Journal of Global Optimization, pages 1-19, 2015. [Link] [arXiv] [BibTex]
  14. Proximal heterogeneous block implicit-explicit method and application to blind ptychographic diffraction imaging with R. Hesse, D.R. Luke & S. Sabach. SIAM Journal on Imaging Sciences, 8(1):426-457, 2015. [Link] [arXiv] [BibTex]
  15. Norm convergence of realistic projection and reflection methods with J.M. Borwein & B. Sims. Optimization, 64(1):161-178, 2015. [Link] [arXiv] [BibTex]
  16. The cyclic Douglas-Rachford method for inconsistent feasibility problems with J.M. Borwein. Journal of Nonlinear and Convex Analysis, 16(4):573-584, 2015. [Link] [arXiv] [BibTex]
  17. Douglas-Rachford feasibility methods for matrix completion problems with F.J. Aragón Artacho & J.M. Borwein. The ANZIAM Journal, 55(4):299-326, 2014. [Link] [arXiv] [BibTex]
  18. Recent Results on Douglas-Rachford methods for combinatorial optimization problems with F.J. Aragón Artacho & J.M. Borwein. Journal of Optimization Theory and Applications, 163:1-30, 2014. [Link] [arXiv] [BibTex]
  19. Recent Results on Douglas-Rachford methods with F.J. Aragón Artacho & J.M. Borwein. Serdica Mathematical Journal, 39:313-330, 2013. [Link] [BibTex]
  20. A cyclic Douglas-Rachford iteration scheme with J.M. Borwein. Journal of Optimization Theory and Applications, 160(1):1-29, 2014. [Link] [arXiv] [BibTex]
  21. 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 & R. Atkin. The Journal of Physical Chemistry C, 115(14):6855-6863, 2011. [Link] [BibTex]
  1. Higher-dimensional wavelets and the Douglas-Rachford algorithm with D. Franklin & J.A. Hogan. In 13th International Conference on Sampling Theory and Applications (SampTA), 2019. [Link] [BibTex]
  2. Characterizations of super-regularity and its variants with A. Daniilidis & D.R. Luke. In Splitting Algorithms, Modern Operator Theory and Applications, Springer, 2019. [arXiv] [BibTex]
  3. Relaxed cyclic Douglas-Rachford algorithms for nonconvex optimization with D.R. Luke & A‑L. Martins. In ICML 2018: Workshop: Modern Trends in Nonconvex Optimization for Machine Learning, 2018. [Link] [BibTex]
  4. Reflection methods for inverse problems with application to protein conformation determination with J.M. Borwein. In Generalized Nash Equilibrium Problems, Bilevel Programming and MPEC, Springer Singapore, 2018. [Link] [arXiv] [BibTex]
  5. Improved stockyard management strategies for coal export terminals at Newcastle with N. Boland, D. Gulczynski, M.P. Jackson & M.W.P. Savelsbergh. In Proceedings of the 19th International Congress on Modelling and Simulation, pages 718-724, 2011. [Link] [BibTex]

Selected Talks

  1. Symbolic convex analysis, CARMA Seminar at U. Newcastle, May 2017 [PDF]
  2. Algorithms for blind ptychographic imaging, CARMA Workshop on Mathematics and Computation at U. Newcastle, June 2015 [PDF]
  3. 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]
  4. Reflection methods for Euclidean distance matrix reconstruction, Australian - New Zealand Mathematics Convention at U. Melb., Dec 2014. [PDF] [Video]
  5. Visualizing projection algorithms, ICERM Challenges in 21st Century Experimental Mathematical Computation Workshop at Brown U., July 2014. [PDF] [Video]
  6. Cyclic Douglas-Rachford iterations, AustMS Annual Meeting at U.Syd, Sept-Oct 2013. [PDF]
  7. Douglas-Rachford for combinatorial optimisation, AMSSC at ANU, July 2013. [PDF]