School of Science, Engineering and Information Technology

Deterministic Algorithms for Large-Scale Computation and Multi-Level Optimization

Project Title:

Deterministic Algorithms for Large-Scale Computation and Multi-Level Optimization

Supervisor(s):

David Yang Gao, Alex Rubinov Professor of Mathematics, Federation University

Tudor Ratiu, Honorary Professor, Shanghai Jiao Tong University

Ron G. Chen, Honorary Professor, City University, Hong Kong

Shu-Cherng Fang, Honorary Professor, North Carolina State University, USA

Eldar Hajilarov, Lecturer

Ning Ruan, Senior Research Fellow

Vittorio Latorre, Research Fellow

Contact person and email address:

David Yang Gao, d.gao@federation.edu.au

A brief description of the project:

Continuously supported by multi-million dollar grants from US Air Force Office for Scientific Research (AFOSR) over the past 10 years, our goal is to conduct a unique pioneering research in the multidisciplinary fields of

  • nonconvex science;
  • large-scale computational mathematics;
  • industrial and systems engineering.

The nonconvexity is essential in natural phenomena. It is the main reason that leads to chaos in complex dynamics, phase transitions in material science, bifurcation in nonlinear systems, fundamental difficulties in game theory and decision-making, as well as many NP-hard problems in global optimisation and computer science. Composed by the pioneering researchers and world well-known scholars in applied mathematicians, computer science, and systems engineering, our group has developed internationally recognised research in nonconvex science with successfully applications in multidisciplinary fields of applied mathematics, engineering mechanics, operations research, global optimisation, decision and computer science.  We are continuously providing breakthrough theories, methods, and computational techniques for young people to conduct cutting-edge research projects in multidisciplinary fields of applied mathematics and engineering sciences.

Research Project

Deterministic Algorithms for Large-Scale Computation and Multi-Level Optimization

In multi-scale complex systems and computer science, many challenging nonlinear equilibrium equations can be reformulated as certain nonconvex/discrete optimisation problems via either variational principles or the least squares method. Conventional numerical analysis and direct approaches can’t solve these problems deterministically due to the lack of global optimality condition. The well-known deterministic methods can’t solve nonconvex/discrete minimisation problems in polynomial time. Therefore, most nonconvex minimisation problems are considered as NP-hard in global optimisation and computer sciences. Unfortunately, this fundamental difficulty is not fully recognised in computational mathematics/mechanics due to the significant gap between these fields.

The main goal of this project is to develop deterministic method and polynomial-time algorithms for solving challenging nonconvex and discrete problems in multidisciplinary fields of computational mathematics and mechanics with real-world applications, particularly in topology design of large-scale complex networks and large deformed structures, etc.