About Yaxiang Yuan’s work
Yaxiang Yuan held a Croucher Visitorship at Hong Kong Baptist University from January to May 1994. At the time, Yuan was based at the Chinese Academy of Sciences.
Biography
Yaxiang Yuan entered Xiangtan University in 1978 and was admitted to the Computing Center of the Chinese Academy of Sciences as a graduate student four years later. He worked at Fitzwilliam College, University of Cambridge (Rutherford Research Fellow) from 1985 to 1988. Yuan has achieved important results in nonlinear optimisation calculation methods and theories. His research results in nonlinear programming are internationally named Yuan's Lemma. His contributions mainly focus on three aspects: trust region method, quasi-Newton method and conjugate gradient method.
The work done in the trust region method algorithm design and convergence analysis is pioneering. In particular, the research on the trust region method of non-smooth optimisation has led to a series of important convergence theorems and provided sufficient conditions for superlinear convergence. He gave the optimality conditions for the double-sphere trust region subproblem and proved the 1/2 conjecture of the truncated conjugate gradient method. In terms of theoretical research on quasi-Newton methods, he collaborated with American scientists to prove the global convergence of a class of quasi-Newton methods.