Algebraic Geometry, Approximation and Optimisation

David Wood

  •  5 Feb 2018 - 16 Feb 2018
     8:00 am - 5:00 pm

Organisers: Enrico Carlini (Politecnico di Torino), Jochen Garcke (University of Bonn), Wolfgang Hackbusch (Max Planck Institute), Markus Hegland (Australian National University), Vera Roshchina (RMIT University), Nadezda Sukhorukova (Swinburne University of Technology), Julien Ugon (Federation University Australia), David Smyth (Australian National University).

Program Description:
There has been notable success in applying the tools of algebraic geometry to a selection of approximation and optimisation problems. In optimisation, a whole new field of convex algebraic geometry has emerged based on the ideas of semidefinite programming relaxations of polynomial problems pioneered by J.-B. Lasserre. However, some notoriously difficult problems are still open, for instance, the optimisation problems arising from multivariate polynomial approximation, and Smale’s 7th problem, need new approaches that combine approximation, optimisation and algebraic geometry. The work in numerical analysis and approximation has been motivated by the success of low rank matrix approximations based on the matrix singular value decomposition which is related to principal component analysis. Yet, these perspective have seldom been combined into a unified approach, but experts have largely been working in parallel. This workshop aims at bringing together these alternative perspective from all three areas to develop collaborative investigations of these problems.

Program Details and Materials:
Program Structure. (Please click on the image to enlarge).

(Please click on the name for the full presentation pdf.)


  • Deadline: 5 January 2018
  • Registration is by invitation only

Participant List:

– Pablo Parrilo (MIT)
– Levent Tuncel (Waterloo)
– Terry Rockafellar (University of Washington)
– Ludmila Polyakova (Saint-Petersburg State University, Russia)
– Wolfgang Hackbusch (Max Planck Institute for Mathematics in the Sciences)
– Enrico Carlini (Politecnico di Torino, Italy)
– Andrew Eberhard (RMIT University)
– Jochen Garcke (Institut für Numerische Simulation)
– Lars Grasedyck (RWTH Aachen University , Aachen)
– Markus Hegland (ANU)
– Vera Roshchina (RMIT University)
– James Saunderson (Monash University)
– Nadezda (Nadia) Sukhorukova (Swinburne University of Technology)
– Julien Ugon (Federation University Australia)
– David Yost (Federation University Australia)
– Alex Kruger (Federation University Australia)
– Fei Lu (RMIT University)
– Thi Bui Hoa (Federation University Australia)
– Scott Lindstrom (CARMA, University of Newcastle)
– Abhishek Bhardwaj (ANU)
– Sebastian Kraemer (RWTH Aachen University , Aachen)
– Nguyen Duy Cuong (Federation University Australia)
– Anand Rajendra Deopurkar (ANU)
– Zari Dzalilov (Federation University Australia)
– Kyle Broder (ANU)
– Shilu Feng (ANU)
– Edda Koo (University of Sydney)


MATRIX Wine and Cheese Afternoon 6 February 2018
On the first Tuesday of each program, MATRIX provides a pre-dinner wine and cheese afternoon. Produce is locally-sourced to showcase delicacies from the region.