## SIAM Awards Lagrange Prize to Roger Fletcher, Sven Leyffer, and Philippe L. Toint

**July 20, 2006**

Established in 2002, the Lagrange Prize in Continuous Optimization is awarded jointly by the Mathematical Programming Society (MPS) and the Society for Industrial and Applied Mathematics (SIAM). SIAM awarded the Lagrange Prize at their annual meeting held in Boston from July 10–14, 2006.

The recipients of this year's prize are Roger Fletcher of the University of Dundee, Scotland, Sven Leyffer of Argonne National Laboratory, and Philippe L. Toint of the University of Namur, Belgium.

The prize is awarded for outstanding works in the area of continuous optimization. Judging of works is based primarily on their mathematical quality, significance, and originality. Clarity and excellence of the exposition and the value of the work in practical applications may be considered as secondary attributes.

The 2006 recipients were recognized on behalf of their papers: "Nonlinear Programming Without A Penalty Function" by Roger Fletcher and Sven Leyffer, published in Mathematical Programming, 91 (2), pp. 239-269 (2002) and "On the Global Convergence of a Filter-SQP Algorithm" by Roger Fletcher, Sven Leyffer, and Philippe L. Toint, published in SIAM Journal on Optimization, Volume 13, pp. 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.

The Society for Industrial and Applied Mathematics (SIAM) was founded in 1952 to support and encourage the important industrial role that applied mathematics and computational science play in advancing science and technology. Along with publishing top-rated journals, books, and *SIAM News*, SIAM holds about 12 conferences per year. There are also currently 45 SIAM Student Chapters and 15 SIAM Activity Groups.

SIAM's 2006 Annual Meeting themes included dynamical systems, industrial problems, mathematical biology, numerical analysis, orthogonal polynomials and partial differential equations.

For complete details, go to http://www.siam.org/meetings/an06/index.php .

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