2006
Lagrange Prize in Continuous Optimization 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.239269 (2002), and
Roger Fletcher, Sven Leyffer, and Philippe L. Toint, "On the
global convergence of a filterSQP algorithm", SIAM
J. Optimization, volume 13, pages 4459, 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 derivativefree 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 nonSQP 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.
