2006 Lagrange Prize Citation
The 2006 Lagrange Prize in Continuous Optimization was awarded by The Mathematical Programming
Society and the Society for Industrial and Applied Mathematics to Roger Fletcher, Sven
Leyffer, and Philippe L. Toint, for the papers
Roger Fletcher and Sven Leyffer, "Nonlinear programming without a penalty
function" Mathematical Programming Mathematical Programming, 91 (2), pp.239-269 (2002), and
Roger Fletcher, Sven Leyffer, and Philippe L. Toint, "On the global
convergence of a filter-SQP algorithm", SIAM J. Optimization, volume 13, pages 44-59, 2002.
In the development of nonlinear programming over the last decade, an outstanding new idea has been
the introduction of the filter. This new approach to balancing feasibility and optimality has been
quickly picked up by other researchers, spurring the analysis and development of a number of
optimization algorithms in such diverse contexts as constrained and unconstrained nonlinear
optimization, solving systems of nonlinear equations, and derivative-free optimization. The generality
of the filter idea allows its use, for example, in trust region and line search methods, as well as in
active set and interior point frameworks. Currently, some of the most effective nonlinear optimization
codes are based on filter methods. The importance of the work cited here will continue to grow as
more algorithms and codes are developed.
The filter sequential quadratic programming (SQP) method is proposed in the first of the two cited
papers. Many of the key ideas that form the bases of later non-SQP implementations and analyses are
motivated and developed. The paper includes extensive numerical results, which attest to the potential
of the algorithm.
The second paper complements the first, using novel techniques to provide a satisfying proof of
correctness for the filter approach in its original SQP context. The earlier algorithm is simplified,
and in so doing the analysis plays its natural role with respect to algorithmic design.