Dr. Sven Leyffer

Argonne National Laboratory

For more information please contact  Dr. Alex Gray; agray@cc.gatech.edu

"A Tale of Two Problems: Integer and Nonlinear Optimization"

Abstract:
Many scientific and engineering applications involve both discrete decisions and nonlinear dynamics that affect the optimality of the final design.  Mixed-integer nonlinear programs (MINLPs) combine the difficulty of discrete variable sets with the challenges of nonlinear functions. The discrete components of an MINLP model phenomena such as fixed charges, dichotomies, and general logical relationships.  Nonlinearities often describe phenomena such as covariance, economies of scale, or physical properties such as pressure, stress, and equilibrium.  We survey recent advances in branch-and-cut methods that have resulted in the new solver FilMINT. Our solver combines MINTO's framework for MILP with filterSQP for nonlinear programs. It updates the MILP branch-and-cut tree with new linearization cuts, integrating modern MIP techniques.  Time permitting we will comment on recent developments for solving nonconvex MINLPs. We present a new method, branch-and-refine that decomposes the nonlinear functions into one- and two- dimensional components for which piecewise linear envelopes are constructed using ideas similar to special ordered sets. The resulting relaxation is then successively refined by branching on integer or continuous variables.

Bio:
Sven is a computational mathematician at Argonne National Laboratory, a fellow of the Computation Institute at the University of Chicago, and an adjunct professor at Northwestern University. He received his PhD in 1994 from the University of Dundee, UK. He serves on the editorial board of three optimization journals (SIAM Journal on Optimization, Computational Optimization and Applications, and Computational Management Science). He is editor-in-chief of Mathematical Methods of Operations Research and coordinating editor for nonlinear optimization of Mathematical Programming Computation. He has also edited two special issues for Mathematical Programming. He was the INFORMS Optimization vice-chair for nonlinear programming, and currently serves as the program director of the SIAM activity group on optimization. He has been on the organizing committee of ICCOPT-07, and was the co-chair of the SIAM Optimization conference in 2008. In 2006, he was awarded the Lagrange prize in optimization (together with Roger Fletcher and Philippe L. Toint). This prize is awarded every three years jointly by the Society for Industrial and Applied Mathematics and the Mathematical Programming Society.

Sven is interested in the development of reliable methods for solving large-scale nonlinear optimization problems and in the implementation and analysis of filter type algorithms. This forms the basis from which he is extending nonlinear optimization methodologies to emerging areas such as mixed-integer nonlinear optimization and optimization problems with complementarity constraints.

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