Prof. YUAN Yaxiang was elected as a new CAS (Chinese Academy of Sciences) academician.
Prof. YUAN Yaxiang is recognized for his contributions to nonlinear optimization, particularly on trust region methods, quasi-Newton methods and nonlinear conjugate gradient methods. On trust region methods, he gave the fundamental theoretical result of the optimal conditions for the Celis-Dennis-Tapia problem, and proved the interesting result that the step obtained by the truncated conjugate gradient method (Steihaug-Toint method) will reduce the quadratic objective function by at least a half of the maximal reduction in the whole trust region ball. On quasi-Newton methods, jointly with Richard Byrd and Jorge Nocedal, he proved the global convergence of the convex Broyden family of quasi-Newton methods, except the DFP method. On nonlinear conjugate gradient methods, he and his student Yuhong Dai gave the new nonlinear conjugate gradient method, called the “Dai-Yuan method”, which is widely regarded as one of the four famous nonlinear conjugate gradient methods.
Prof. YUAN received numerous awards, including L. Fox Prize in 1985, the Feng Kang Scientific Computing Prize in 1995, the Young Scientist Award of China and China National Funds for Distinguished Young Scientists in 1996, “China Top 10 Outstanding Youth” award in 1998, National Excellent Science and Technology Worker in 2005, the second Prize of National Natural Science Award in 2006, the Shiing- Shen Chern Mathematics Award of Chinese Mathematical Society in 2011. He gave a plenary lecture at the 4th International Congress on Industrial and Applied Mathematics (ICIAM-99) held in Edinburgh in 1999, and was elected as a Fellow of the Society for Industrial and Applied Mathematics (SIAM) in 2011. Prof. YUAN served as one of the vice-presidents of Chinese Mathematical Society from 2000 to 2007, one of the vice presidents of China Society for Industrial and Applied Mathematics from 2000 to 2008, and is currently the President of the Operations Research Society of China.