| Citation | Distinguished for his highly original research in nonlinear optimisation and numerical algorithms. He pioneered the variable metric and conjugate gradient methods for problems without constraints. He achieved a major breakthrough, when there are constraints, by inventing the first exact differentiable penalty function which forces convergence even when the initial state is not well chosen. Another remarkable first, his `filter method', provides global convergence yet is much more versatile than penalty function methods. He has initiated many powerful algorithms which are deployed in quadratic programming, integer programming, updating matrix factorisation and dealing with degeneracies in linear programming. International recognition of his outstanding record occurred in the award of the prestigious Dantzig Prize for Optimization from the Mathematical Programming Society and the US Society for Industrial and Applied Mathematics in 1997. The numerous computer programs, based on his work, which are in widespread use today are yet another testimony to the enormous significance and invaluable nature of the research he has carried out. |