Prof. Michael James David Powell, a Fellow of the Royal Society, from Cambridge University gave the lecture named “A parsimonious way of constructing quadratic models from values of the objective function in derivative-free optimization” at AMSS on Nov.4, 2011. More than 100 researchers and graduates of National Center for Mathematics and Interdisciplinary Sciences (NCMIS), CAS attended the event. Prof. YUAN Yaxiang presided over the meeting.

In his talk, he considered the so-called Derivative Free Optimization problems in which we minimized a function without the information of its first order derivatives. He attacked this problem by constructing a trust region model based on interpolation. First he considered the linear model which was constructed by interpolating the objective function at n+ 1 point on each iteration. An algorithm of this kind was described briefly with a convergence theorem. Then he presented a technique in which we can construct a quadratic model by using only n+1 interpolation points on each iteration as well. Experiments demonstrated that this technique for constructing quadratic models provided major improvements over the use of linear models, both in the total number of function evaluations and in the final accuracy of the optimization calculation.

Prof. Michael James David Powell from Cambridge University is a fellow of the Royal Society, and also a founding member of the Institute of Mathematics and its Applications and a founding Managing Editor of the Journal for Numerical Analysis. He is well known for his extensive work in numerical analysis, especially nonlinear optimization and approximation. He was the winner of many awards, including George B. Dantzig Prize from the Mathematical Programming Society/SIAM and the Naylor Prize from the London Mathematical Society.