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.