Powell was known for his extensive work in
numerical analysis, especially
nonlinear optimisation and
approximation. He was a founding member of the
Institute of Mathematics and its Applications and a founding editor-in-chief of
IMA Journal of Numerical Analysis. His mathematical contributions include
quasi-Newton methods, particularly the
Davidon–Fletcher–Powell formula and the Powell's Symmetric Broyden formula,
augmented Lagrangian function (also called Powell–
Rockafellar penalty function),
sequential quadratic programming method (also called as Wilson–Han–Powell method),
trust region algorithms (
Powell's dog leg method),
conjugate direction method (also called
Powell's method), and
radial basis function. He had been working on
derivative-free optimization algorithms in recent years, the resultant algorithms including COBYLA, UOBYQA, NEWUOA, BOBYQA, and LINCOA. He was the author of numerous scientific papers
Awards and honours Powell won several awards, including the
George B. Dantzig Prize from the Mathematical Programming Society/
Society for Industrial and Applied Mathematics (SIAM) and the
Naylor Prize from the
London Mathematical Society. Powell was elected a
Foreign Associate of the National Academy of Sciences of the United States in 2001 and as a corresponding fellow to the
Australian Academy of Science in 2007. == References ==