Research Center
- Center for Numerical Simulation & Modeling
RESEARCH AREAS
(Some of
links are closed due to the space limitation)
Dr. Gao studies modeling,
methods, and theories of duality, triality,
as well as some of closely related concepts (such as complementarity, polarity, symmetry and
symmetry breaking, etc.) in science, engineering, and computation, with
applications to general complex systems, including nonconvex/nonsmooth and
nonconservative problems in nonlinear analysis, global optimization and
control, differential equations and geometry, finite deformation field theory, engineering
mechanics, network flows and communications, and to large scale scientific
computations. His work on duality theory in convex systems emphasizes how it
relates to a unified framework in natural phenomena with symmetry; while the
work on triality in non-convex systems aims to understand symmetry
breaking, to reveal intrinsic duality, and to discover general pattern of
duality in complex systems. His multi-disciplinary research activities
were supported by Divisions of Mathematical Science (DMS), Civil and Structural
Engineering (CMS), Operations Research & Production Systems (DMII), and
Computer & Information Science & Engineering (CCF) at National Science
Foundation. Currently he has two active NSF grants with total $210,000 for
2005-2008.
Dr. Gao was trained in the fields of Engineering Science and Applied
Mathematics. His research interests range over the following areas:
- Applied Mathematics
- Applied Nonconvex and nonsmooth Analysis
- Variational Methods and Variational Inequality
- Nonconservative
- Optimization and Control
- Global Optimization
- Integer and fractional Programming, semi-infinite programming
- Optimal design and simulation of complex systems
- Dual feedback control of distributed parametrical systems
- System Engineering and Management Science
- Modeling and analysis of complex systems
- Understand and control chaotic systems
- Canonical System theory
- Decision making in management
- Optimization in Network and Communication Theory (including sensor localization, max cut, etc)
- Theoretic and Applied Mechanics
- Finite Deformation Modeling and Theory
- Nonsmooth/Nonconvex Mechanics
- Elasto-plastic Structural Limit Analysis
- Contact Mechanics
- Structural Optimal Design
- Phase transitions in solids
- Scientific Computation
- Primal-Dual Algorithms for solving nonconvex/nonsmooth problems
- Canonical dual finite element methods
- Large Scale Scientific Computations and simulations
- Duality, Complementarity and Triality in Sciences and Philosophy
Recent
research results:
- Complete solutions to a class of global optimization problems
- Complete solutions to a nonconvex quadratic minimization problem over a sphere
- Complete solution to concave minimization with quadratic inequality constraint
- Pure Complementary Energy Variational Principle of Nonlinear Elasticity
- Large deformation elastic beam models: 1. static model , 2. dynamical models
- bi-duality and bi-complementarity theories in variational inequalities and non-convex optimization;
- tri-duality and canonical dual transformation method for solving general fully nonlinear systems, global optimization;
- general analytic solution for nonconvex/nonsmooth variational problems and
- General Solutions for large deformation elasto-plastic problems;
- polarity principle in nonconvex, nonconservative Hamilton systems ;
- dual feedback control against chaos
- new phenomena in chaotic systems: meta-chaos and trio-chaos.
Editorial:
- Co-Editor-in-Chief for two book series:
- Springer Book Series: Advances in Mechanics and Mathematics (AMMA)
- Chapman & Hall/CRC Book Series: Modern Mechanics and Mathematics (MMM)
- Associate Editor for the following journals
Organizations and Activity Research Groups:
- American Academy of Mechanics
- Complementarity problem network for Mathematical programming
- INFORMS
- MASIE:
Mechanics and Symmetry in
- Mathematical Programming Society
- Optimization Research Bridge
- Pacific Optimization Research Activity Group(POP)
- SIAM Society for Industrial and Applied Mathematics
Some movies about finite
element simulations for dynamical post-buckling analysis of a rubber
diaphragm created by my Ph.D. student Axinte Ionita:
Publications
Complete publications list
Publications listed by research areas
- Gao, David Y., Duality-Mathematics, Wiley Encyclopedia of Electronical and Eletronical Engineering 6, 1999, 68-77 ps file
- Gao, David Y., Mono-duality in Convex Systems, ENCYCLOPEDIA OF OPTIMIZATION, Kluwer Academic Publishers
- Gao, David Y., Bi-duality in convex dynamically systems and D.C. programming, ENCYCLOPEDIA OF OPTIMIZATION, Kluwer Academic Publishers
- Gao, David Y., Triality in Global Optimization, ENCYCLOPEDIA OF OPTIMIZATION, Kluwer Academic Publishers
- Gao, David Y., Dao of the complementarity-duality: I. Complementarity and dual principles in natural sciences, in Selected Philosophical Papers of Tsinghua's Ph.D. Thesis, Tsinghua Univ. Press, 1996
- Gao,
D.Y., Dao of the complementarity-duality: II. Complementarity
and dual principles in general systems. Excellent paper award in The
First National Congress on Natural Philosophy,
Grant Agents:
Links
Optimal Shape Design for extended beam model.
Back to the home of David
Yang Gao
E-mail to me at gao at vt.edu