I am a post-doctoral researcher at the Institute for Numerical and Applied Mathematics at the University of Göttingen supported by a fellowship from the Alexander von Humboldt Foundation. Previously, 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".
My primary research interests lie mostly within the field of continuous optimisation. The mathematical problems which most interest me are those which reconcile mathematical theory, mathematical modelling, algorithms and applications.
- Algorithms based on unions of nonexpansive maps, Optimization Letters, to appear. DOI: 10.1007/s11590-018-1249-7 Preprint: arXiv:1710.08227
- A Lyapunov-type approach to convergence of the Douglas-Rachford algorithm with M.N. Dao. Preprint: arXiv:1706.04846
- A feasibility approach for constructing combinatorial designs of circulant type with F.J. Aragón Artacho, R. Campoy and I. Kotsireas. Journal of Combinatorial Optimization, to appear. DOI: 10.1007/s10878-018-0250-5 Preprint: arXiv:1711.02502
- Implicit error bounds for Picard iterations on Hilbert spaces with D.R. Luke and Nguyen H.T.. Vietnam Journal of Mathematics, to appear. DOI 10.1007/s10013-018-0279-x
- Symbolic computation with monotone operators with F. Lauster and D.R. Luke. Set-Valued and Variational Analysis, to appear. DOI: 10.1007/s11228-017-0418-7 Preprint: arXiv:1703.05946.
- Quantitative convergence analysis of iterated expansive, set-valued mappings with D.R. Luke and Nguyen H.T.. Mathematics of Operations Research, to appear. Preprint: arXiv:1605.05725.
- Convergence rate analysis for averaged fixed point iterations in common fixed point problems with J.M. Borwein and G. Li. SIAM J. Optim., 27(1):1-33, 2017. DOI: 10.1137/15M1045223 Preprint: arXiv:1510.06823.
- Regularity properties of non-negative sparsity sets. J. Math. Anal. and Appl., 447(2):758--777, 2017. DOI: 10.1016/j.jmaa.2016.10.040 Preprint: arXiv:1607.05924.
- Global behavior of the Douglas-Rachford method for a nonconvex feasibility problem with F.J. Aragón Artacho and J.M. Borwein. J. Glob. Optim., 65(2):309-327, 2016. DOI: 10.1007/s10898-015-0380-6 Preprint: arXiv:1506.09026.
- Reflection methods for inverse problems with application to protein conformation determination with J.M. Borwein. Springer volume on the CIMPA school Generalized Nash Equilibrium Problems, Bilevel programming and MPEC New Delhi, India, Dec. 2012. Submitted August 2014. ISSN: 978-981-10-4774-9 Preprint: arXiv:1408.4213
- Proximal heterogeneous block input-output method and application to blind ptychographic diffraction imaging with R. Hesse, D.R. Luke and S. Sabach. SIAM J. Imaging Sci. 8(1):458-483, 2015. DOI: 10.1137/14098168X Preprint: arXiv:1408.1887
- Norm convergence of realistic projection and reflection methods with J.M. Borwein and B. Sims. Optim., 64(1):161-178, 2015. DOI: 10.1080/02331934.2014.947499. Preprint: arXiv:1312.7323
- The cyclic Douglas-Rachford method for inconsistent feasibility problems with J.M. Borwein. J. Nonlinear Convex Anal., 16(4):537-584, 2015. Preprint: arXiv:1310.2195
- Douglas-Rachford feasibility methods for matrix completion problems with F.J. Aragón Artacho and J.M. Borwein. ANZIAM J. 55(4):299-326, 2014. DOI: 10.1017/S1446181114000145, Preprint: arXiv:1308.4243.
- Recent results on Douglas-Rachford methods for combinatorial optimization problems with F.J. Aragón Artacho and J.M. Borwein. J. Optim. Theory Appl., 163(1):1-30, 2014. DOI: 10.1007/s10957-013-0488-0. Preprint: arXiv:1305.2657.
- Recent results on Douglas-Rachford methods with F.J. Aragón Artacho and J.M. Borwein. Serdica Math. J., 39:313-330, 2013.
- A cyclic Douglas-Rachford Iteration Scheme with J.M. Borwein. J. Optim. Theory Appl., 160(1):1-29, 2014. DOI: 10.1007/s10957-013-0381-x. Preprint: arXiv:1303.1859.
- Improved stockyard management strategies for coal export terminals at Newcastle with N. Boland, D. Gulczynski, M.P. Jackson and M.W.P. Savelsbergh. MODSIM2011, 19th International Congress on Modelling and Simulation, 1652-1658, 2011.
- 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. J. Phys. Chem. C, 115(14):6855-6863, 2011. DOI: 10.1021/jp200544b.
- Algorithms based on unions of nonexpansive maps, GAMM Annual Meeting, Munich, March 2018 [PDF]
- Symbolic convex analysis, CARMA Seminar at U. Newcastle, May 2017 [PDF]
- Algorithms for blind ptychographic imaging, CARMA Workshop on Mathematics and Computation at U. Newcastle, June 2015 [PDF]
- 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]
- Reflection methods for Euclidean distance matrix reconstruction, Australian - New Zealand Mathematics Convention at U. Melb., Dec 2014. [PDF] [Video]
- Visualizing projection algorithms, ICERM Challenges in 21st Century Experimental Mathematical Computation Workshop at Brown U., July 2014. [PDF]
- Cyclic Douglas-Rachford iterations, AustMS Annual Meeting at U.Syd, Sept-Oct 2013. [PDF]
- Douglas-Rachford for combinatorial optimisation, AMSSC at ANU, July 2013. [PDF]