Sven Leyffer (left) and Ariela Sofer.
The 2016 Farkas Prize is awarded to Sven Leyffer, senior computational mathematician from Argonne National Laboratory, for his fundamental contributions to the design and analysis of computational algorithms for large-scale nonlinear optimization and mixed-integer nonlinear optimization problems.
In his PhD thesis under the direction of the late Roger Fletcher, Leyffer made significant contributions in extending the outer approximation method developed by Duran and Grossmann for solving mixed Integer nonlinear programming (MINLP) problems. The work allowed a much wider class of problems to be tackled, including the case when the problem involves nonlinear integer variables, and provided a rigorous treatment of infeasibilities and convergence proof to the methodology. Subsequently, he laid the ground for the first SQP-based branch and bound method for MINLP.
In later groundbreaking work with Roger Fletcher, Leyffer proposed a new class of methods for constrained nonlinear programs, which employ the innovative concept of a filter for balancing between feasibility and optimality, and which builds on the concept of domination from multi-objective optimization. This new approach, which has proven to be highly effective, has had a profound influence on nonlinear programming, and has sparked much research among optimizers. Originally proposed within the context of a trust-region SQP algorithm for continuous optimization, it has been extended to non-SQP algorithms, and has also sparked the development of new algorithms and software for nonsmooth optimization, derivative-free optimization and nonlinear equations.
Another fruitful direction that Leyffer has taken is the solution of optimization problems with complementarity constraints formulated as nonlinear programs. He showed that adding the complementarity conditions as a penalty in the objective instead of treating them as constraints is highly effective, and also reported solutions using this approach with interior point methods.
Together with his contributions to theory and computational algorithms Leyffer has made strong contributions in the development of practical and freely available software. These include the NEOS software packages “filter” (with Fletcher) for the solution of nonlinearly constrained problems, and the packages MINLP and FilMINT (also coauthored), which illustrate different implementations of the outer-approximation method for MINLPs. He has also embarked as a coauthor on the very ambitious project MINOTAUR, a tool kit for open-source software for solving MINLP problems.
For all his contributions, Sven Leyffer is eminently deserving of the 2016 Farkas Prize awarded by the Optimization Society within the Institute for Operations Research and Management Science.
Ariela Sofer (chair), Ignacio Grossmann, Ted Ralphs, Alex Shapiro