Polynomial Optimization based on Sums-of-Squares and Difference-of-Convex Programming Approaches
发布者：季洁发布时间：2019-11-20浏览次数：113
| Speaker: | Yi-Shuai Niu, Shanghai Jiao Tong University |
| Host: | Rujun Jiang, School of Data Science, Fudan University |
| Time: | 16:00-17:00, Nov 25, 2019 |
| Location: | Room 102, Zibin Building, Fudan University |
| Abstract: | Polynomial optimization is a special case of DC (Difference-of-Convex) program, however finding a DC representation for a multivariate polynomial is difficult. We will focus on polynomial decomposition techniques based on sums-of-squares in order to represent any multivariate polynomial as difference-of-sums-of-squares (DSOS) and difference-of-convex-sums-of-squares (DCSOS). We will show that the set of DSOS and DCSOS polynomials are vector spaces, and any polynomial can be represented as DSOS and DCSOS. We also prove that the constructions of DSOS and DCSOS decompositions are equivalent to solve semi-definite programs (SDP) which can be achieved in polynomial time. Then, we will focus on establishing several practical algorithms (Parity Decompositions and Spectral Decompositions) for DSOS and DCSOS without solving SDP. Some examples illustrate how to use our methods. Finally, we also propose a DC programming approach based on DCSOS decomposition to solve polynomial optimization over a convex set. |
| Bio: | Yi-Shuai Niu holds a professor at Shanghai Jiao Tong University (SJTU), joint faculty in the SJTU-Paristech Elite Institute of Technology, and the School of Mathematical Sciences. His researches are mainly focused on Optimization (Difference-of-Convex Programming, Polynomial Optimization, Mixed-Integer Optimization and Semi-Definite Programming), and high performance computing in multidisciplinary sciences (Portfolio Investment, Deep Neural Network, Turbulent Combustion, and Quantum Chemistry). He received double master degrees: Pure and Applied mathematics, and engineering mathematics from the “Grand école” National Institute of Applied Sciences in France (2006), and a Ph.D degree in Operations Research from the same University (2010). He had held research positions at National Institute of Applied Science (2007-2012), French National Center for Scientific Research (CNRS) and Stanford University (2010-2012), and University of Paris 6 (2013-2014). He received the Outstanding Teaching Award in Shanghai in 2017, Teaching Achievement Award at SJTU in 2016, and INFORMS best paper award for MCM/ICM contest in 2017. Dr. Niu had published several articles on Computational Optimization and Application, Applied Mathematics and Computation, Combustion and Flame, and Scientific Reports etc. He served as reviewer for several academic journals, including Mathematical Programming, Computational Optimization and Applications, Journal of Global Optimization, and Flow-Turbulence and Combustion. |
