Roger Fletcher was well known for his highly original research in nonlinear optimisation and numerical algorithms, pioneering 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 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 record included the award of the prestigious Dantzig Prize for Optimization from the Mathematical Programming Society, the US Society for Industrial and Applied Mathematics in 1997, and the award of the Royal medal of the Royal Society of Edinburgh in 2008. Numerous computer programs based on his work are in widespread use today.
Professor Roger Fletcher FRS died on 5 June 2016.
Subject groups
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Mathematics
Applied mathematics and theoretical physics, Statistics and Operational Research
