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
- The Douglas-Rachford algorithm for convex and nonconvex feasibility problems with . 2019.
- Shadow Douglas-Rachford splitting for monotone inclusions with . 2019.
- A forward-backward splitting method for monotone inclusions without cocoercivity with . 2018.
- Union averaged operators with applications to proximal algorithms for min-convex functions with . Journal of Optimization Theory and Applications, 1(181):61-94, 2019.
- A feasibility approach for constructing combinatorial designs of circulant type with . Journal of Combinatorial Optimization, 35(4):1061-1085, 2018.
- Algorithms based on unions of nonexpansive maps. Optimization Letters, 12(5):1017-1027, 2018.
- A Lyapunov-type approach to convergence of the Douglas-Rachford algorithm with . Journal of Global Optimization, 73(1):83-112, 2019.
- Implicit error bounds for Picard iterations on Hilbert spaces with . Vietnam Journal of Mathematics, 46(2):243-258, 2018.
- Symbolic computation with monotone operators with . Set-Valued and Variational Analysis, 26:353-368, 2018.
- Regularity properties of non-negative sparsity sets. Journal of Mathematical Analysis and Applications, 447(2):758-777, 2017.
- Quantitative convergence analysis of iterated expansive, set-valued mappings with . Mathematics of Operations Research, published online July 2018.
- Convergence rate analysis for averaged fixed point iterations in common fixed point problems with . SIAM Journal on Optimization, 27(1):1-33, 2017.
- Global behavior of the Douglas-Rachford method for a nonconvex feasibility problem with . Journal of Global Optimization, pages 1-19, 2015.
- Proximal heterogeneous block implicit-explicit method and application to blind ptychographic diffraction imaging with . SIAM Journal on Imaging Sciences, 8(1):426-457, 2015.
- Norm convergence of realistic projection and reflection methods with . Optimization, 64(1):161-178, 2015.
- The cyclic Douglas-Rachford method for inconsistent feasibility problems with . Journal of Nonlinear and Convex Analysis, 16(4):573-584, 2015.
- Douglas-Rachford feasibility methods for matrix completion problems with . The ANZIAM Journal, 55(4):299-326, 2014.
- Recent Results on Douglas-Rachford methods for combinatorial optimization problems with . Journal of Optimization Theory and Applications, 163:1-30, 2014.
- Recent Results on Douglas-Rachford methods with . Serdica Mathematical Journal, 39:313-330, 2013.
- A cyclic Douglas-Rachford iteration scheme with . Journal of Optimization Theory and Applications, 160(1):1-29, 2014.
- Double layer structure of ionic liquids at the Au (111) electrode interface: an atomic force microscopy investigation with . The Journal of Physical Chemistry C, 115(14):6855-6863, 2011.
Conference Proceedings and Book Chapters
- Characterizations of super-regularity and its variants with . In Splitting Algorithms, Modern Operator Theory and Applications, Springer, 2019.
- Relaxed cyclic Douglas-Rachford algorithms for nonconvex optimization with . In ICML 2018: Workshop: Modern Trends in Nonconvex Optimization for Machine Learning, 2018.
- Reflection methods for inverse problems with application to protein conformation determination with . In Generalized Nash Equilibrium Problems, Bilevel Programming and MPEC, Springer Singapore, 2018.
- Improved stockyard management strategies for coal export terminals at Newcastle with . In Proceedings of the 19th International Congress on Modelling and Simulation, pages 718-724, 2011.
- 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] [Video]
- 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]