Organisers:
Hoa Bui (Curtin University)
Minh Dao (RMIT University)
Reinier Díaz Millán (Deakin University)
Guoyin Li (University of New South Wales)
Orizon Perreira Ferreira (Federal University of Goiás, Brazil)
Vinesha Peiris (Curtin University)
Nadezda Sukhurukova (Swinburne University)
Julien Ugon (Deakin University)

Program Description:

This meeting will aim to foster collaboration between researchers working in the broader field of generalised convexity, as well as researchers in optimisation algorithms, with the view of generating progress on the development of nonconvex optimisation algorithms. Generalised convexity is a lively discipline with many branches, including quasi- and pseudo-convexity, fractional programming, and abstract convexity. Many researchers participating in this program work on the theoretical aspects of generalised convexity, including obtaining optimality conditions, local and global approximations (generalised subdifferentials), duality, etc. There have also been interesting developments on the development of robust algorithms able to minimise those functions, but much less extensively. At the same time, convex programming is a mature field where significant results have been achieved. Even classical algorithms such as the conditional gradient, alternative projection, or Douglas-Rachford have been extended in various ways. The goal of this program will be to study how these classical and less classical methods can be the basis for nonconvex algorithms, by exploiting the theoretical results from generalised convexity.

The program is structured to maximise interactions between researchers, with strategically targeted morning talks and lectures supporting these discussions on recent developments in central aspects of the research. Quality and topicality of the talks will be favoured over quantity. The first part of the program will focus on open problems to guide the discussions throughout the program. Australian mathematicians have historically been, and continue to be, at the forefront of research in generalised convexity. This MATRIX program will help sustain this expertise while fostering new collaborative projects within the community - both across Australia and on the global stage.

Program Structure:
TBD

Registration:

• Deadline: TBD
• Registration is by invitation only. If you are interested to participate in this program, please contact one of the organisers with your CV and research background.
• Arrival date: 10 February 2027

ASSOCIATED EVENTS
MATRIX Wine and Cheese Afternoon 12 February 2027
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.