News & Announcements

March 22, 2013

"Argonne's Sven Leyffer Presents 2-Week Course in Optimization"

Sven Leyffer, a computational mathematician in the Mathematics and Computer Science Division at Argonne National Laboratory, presented a two-week course February 18– March 1 at the Catholic University of Louvain in Belgium. The theme for the course was "Mixed-Integer Nonlinear Optimization: Applications, Algorithms, and Computation."

Scientists and engineers are increasingly turning from the simulation of complex processes to the optimization and design of complex systems. “Many important design problems involve not only continuous variables but also discrete decisions, giving rise to what we call MINLPs – mixed-integer nonlinear programming problems,” said Leyffer. "The past 10 years or so have seen an increase in new algorithmic approaches and software packages for solving these problems."

The two-week course covered a variety of topics, including algorithms, software, and heuristics for MINLPs and the underlying theory of these algorithms. The students also gained practical experience by evaluating the performance of MINLPs on test problems.

"Applications arise in electrical engineering and the modeling of the power grid, chemical engineering, and communication engineering," Leyffer said. He showed how to model a range of such applications as MINLPs.

A highlight of the course was the presentation of MINOTAUR, a new toolkit developed by Leyffer for solving MINLPs. The modular code enables developers and users to efficiently combine their knowledge of problem structure with algorithmic insights. Leyffer provided examples of how to develop solvers within MINOTAUR, focusing on the integration of nonlinear solvers into the MINOTAUR's branch-and-cut framework.

"Many challenges and open questions in nonlinear optimization remain, offering fruitful ideas for future dissertations," Leyffer told the graduate students. He cited bilevel MINLPs, which arise in leader-follower games, and optimization under uncertainty.

"Emerging exascale architectures also present a host of implementation issues and opportunities," said Leyffer. "Will MINLPs be able to exploit billion-way parallelism? What other models can be leveraged for additional concurrency? All these issues mean that the field is at an exciting stage."