报告时间：2015年6月10日星期三上午10：00
报告地点：浙江大学紫金港校区图书信息中心B楼CAD&CG国家重点实验室402室
报告题目：Canonical Duality-Triality: Unified Modeling, Theory and Solution to Challenging Problems in Complex Systems
报告人：David Yang Gao教授
主持人：李明副教授
Abstract:
Duality is one of the oldest and most beautiful concepts in human knowledge with a simple origin from the oriental philosophy tracing back 5000 years. Canonical duality theory [1,2] is a newly developed, breakthrough methodology, which can be used to model complex systems with a unified solution to a wide class of discrete and continuous problems in engineering sciences. The associated triality theory reveals an interesting multi-scale duality pattern in complex systems, which can be used to identify both global and local extrema and to design powerful algorithms for solving challenging problems in computational sciences.
In this talk, the speaker will first present some fundamental principles for modeling complex systems. Based on the definitions of objectivity and canonical duality in continuum physics, he will show why the complex systems can be modelled within a unified framework, how the canonical duality theory is naturally developed, and the fundamental reasons that lead to challenging problems in different fields, including chaotic dynamics, phase transitions of solids, multi-solutions in post-buckling analysis, and NP-hard problems in global optimization and computational sciences. By using a simple example in phase transitions, he will show that a magic method to obtain a unified analytic solution for general finite deformation problems in both continuum physics and network optimization and to identify both global and local optimality conditions from infinitely many local solutions. A movie will reveal a hidden truth that for many nonconvex variational problems, both global and local extremal solutions are usually nonsmooth, and cannot be captured by any traditional Newton-type direct approaches [3]. Applications will be illustrated by certain well-known challenging problems in nonlinear analysis as well as NP-hard problems in complex systems (such as Einstein’s special relativity equation and post-buckling of large deformed beam). A set of complete analytical solutions to 3-D nonlinear elasticity will be presented [4,5]. Results show that for St. Venant-Kirchhoff material, the nonlinear PDE could have up to 24 solutions at each coordinate, but only one global minimizer. Finally, some open problems and possible methodologies will be addressed.
This talk will bring some fundamentally new insights into nonlinear analysis, complex systems, and computational science.
Bio:
David Y. Gao received his PhD from Tsinghua University. He has held research and teaching positions in different institutes including MIT, Yale, Harvard, University of Michigan, and Virginia Tech. Currently, he is the Alexander Rubinov Chair Professor of Mathematics at Federation
University Australia and a Research Professor of Engineering Science at Australian National University.
Professor Gao’s research interests range over interdisciplinary fields of applied, theoretical and engineering mechanics, operations research and computational science. His main research contributions include a canonical duality-triality theory, a pure complementary energy principle in
nonlinear elasticity, several mathematical models in engineering mechanics and material science, a series of complete solutions to a class of nonconvex/nonsmooth problems in nonlinear analysis and mechanics, and some deterministic methods/algorithms for solving certain NP-hard problems in global optimization and computational science. He is the author of about 10 monograph/handbook/special volumes and more than 170 research papers on mathematical modeling, modern mechanics, applied analysis, nonlinear PDEs, nonconvex/nonsmooth variational methods, large deformation structural theory (beams, plates, and shells), complex dynamical systems, bifurcation theory, phase transitions in solids, global optimization and control, operations research, information theory, decision science, numerical methods and computational science with extensive applications in physics, engineering, and general systems.
Professor Gao is an editor-in-chief for two book series including Advances in Mechanics and Mathematics by Springer. He is also an associate editor of about eight international journals. Since 2000, Professor Gao has delivered over 30 keynote/plenary/invited lectures at international conferences and more than 60 colloquium talks at different universities and institutions.
As the chair and co-chair, he has organized successfully about 10 world congress/conferences. Currently, he is serving as the Secretary-General and Vice President of the International Society of Global Optimization.
