Nathan Krislock

Nathan Krislock received his PhD in Combinatorics and Optimization in 2010 under the supervision of Henry Wolkowicz. The title of his thesis is "Semidefinite Facial Reduction for Low-Rank Euclidean Distance Matrix Completion".

Finding low-rank completions of Euclidean distance matrices is an NP-hard problem with modern applications in wireless sensor network localization and protein structure determination. Approximating low-rank completions for Euclidean distance matrices is possible using semidefinite programming relaxations. However, only small problems can be handled directly using semidefinite relaxations due to the high complexity of semidefinite programming solvers.

Nathan used the idea of facial reduction to reduce the size of the semidefinite relaxations, and was successful in finding exact solutions to sensor network problems with up to a hundred thousand sensors within just a few minutes of computing time. This led to a publication in the SIAM Journal of Optimization. This facial reduction theory also proved useful in protein structure determination and led to a publication in the Journal of Computational Biology.

After completing his PhD at Waterloo, Nathan worked as an INRIA postdoctoral fellow with Jérôme Malick, contributing to the development of the BiqCrunch solver for general binary quadratic optimization problems. He then did a PIMS postdoctoral fellowship with Michael Friedlander in the Department of Computer Science at the University of British Columbia, working on sparse and low-rank recovery methods with connections to semidefinite programming.

Nathan continues to do research in semidefinite programming with a focus on numerical computation and applications. In August 2013, Nathan will be joining the Department of Mathematical Sciences at Northern Illinois University.