Abstract:

From solving PDE-constrained inverse problems to designing the next generation of computer chips, complex nonlinear optimization tasks are prevalent in science and industry.  In this talk we will discuss recent developments in gradient-based nonlinear optimization methods, which have brought about significant advances in the scale and complexity of problems that can be solved in practice.  The goal of this talk is to give a general scientific audience a taste of the types of problems that can now be solved with gradient-based methods and provide an intuition for some of the computational tools that make it possible to solve real-world nonlinear optimization problems with millions of variables and constraints.  To demonstrate the success of these methods, an industrial application considering the optimization of transistor widths in digital circuits will be presented.  This problem is particularly challenging as it combines an analytical problem statement with sophisticated physics-based simulations for computing the transition times in digital circuits.  The presentation will provide an overview of the mathematical properties that underpin these gradient-based methods and introduce the open-source nonlinear optimization package Ipopt as a means to make large-scale nonlinear optimization accessible to a wide variety of problem domain experts.

Bio:

Andreas Wächter is a Professor in the Department of Industrial Engineering and Management Sciences at Northwestern University.  He obtained his master's degree in Mathematics at the University of Cologne, Germany, in 1997, and this Ph.D. in Chemical Engineering at Carnegie Mellon University in 2002.  Before joining Northwestern University in 2011, he was a Research Staff Member in the Department of Mathematical Sciences at IBM Research in Yorktown Heights, NY.  His research interests include the design, analysis, implementation and application of numerical algorithms for nonlinear continuous and mixed-integer optimization.  He is a recipient of the 2011 Wilkinson Prize for Numerical Software and the 2009 Informs Computing Society Prize for his work on the open-source optimization package Ipopt.  Professor Wächter is spending his sabbatical in LANL's Center for Nonlinear Studies (CNLS) as a Ulam Scholar and is excited to learn more about the challenging optimization problems that are faced by LANL scientists.