Leyffer’s accomplishments are in three principal areas: nonlinearly constrained optimization, mixed-integer nonlinear optimization, and optimization problems with equilibrium constraints.
“I am humbled and deeply honored to be selected for this award,” said Leyffer. “The endless variety of optimization problems has long fascinated me – whether involving the creation of complex theory or rigorous algorithms or sophisticated software. I am excited to continuing to work at the bleeding edge of optimization and its numerous applications.”
A senior computational mathematician in the Mathematics and Computer Science Division at Argonne National Laboratory, Leyffer is a world leader in both the theory and the development of numerical optimization. He (with his colleagues) introduced filter methods that provide safeguards for global convergence—an approach to nonlinear programming that has been called the key development in nonlinear optimization of the 1990s. Filter methods today represent a powerful general technique that can be applied in many classes of optimization problems. For this work, Leyffer (and his colleagues) won the prestigious Lagrange Prize in Optimization in 2006, awarded jointly by the Mathematical Optimization Society and the Society for Industrial and Applied Mathematics (SIAM).
Leyffer has also attacked mixed-integer nonlinear optimization programs (MINLPs), considered among the most challenging optimization problems. He (with his colleagues) developed a new and simplified convergence proof for outer approximation, a key algorithm for MINLP, and generalized it to include second-order information. He also coorganized an invited “hot topics” workshop on MINLPs at the Institute of Mathematics and Applications and coedited a book of expository and research papers based on the workshop: Mixed-Integer Nonlinear Optimization: Algorithmic Advances and Applications (Springer, 2012), now considered a major reference for the field. Together with colleagues at Argonne and the University of Wisconsin-Madison, Leyffer developed MINOTAUR, a state-of-the-art software package for solving MINLPs.
An equally challenging class of optimization problems is mathematical programs with complementarity constraints. Leyffer transformed this area, providing both the theoretical foundations explaining the convergence of these problems and—for the first time—reliable, large-scale optimization solvers. He (with his colleagues) has promoted these new solvers by solving leader-follower games in electricity markets.
Moreover, Leyffer has successfully applied his expertise to other complex, real-world problems in optimization. For example, he (with collaborators) has investigated optimal security response to attacks on open science grids); explored oil spill response planning; developed a surrogate-based model of the optical response of metallic nanostructures; and formulated an optimization-based approach that integrates x-ray fluorescence tomography and x-ray transmission data.
Leyffer was named a SIAM Fellow in 2009, as part of SIAM’s first fellowship class. He currently is coeditor of Mathematical Programming and associate editor of Computational Optimization and Applications and is on the editorial board of the SIAM Series on Fundamentals of Algorithms. He also serves as secretary for the International Council for Industrial and Applied Mathematics (ICIAM) and serves on several SIAM committees, such as the SIAM committee on Science Policy.