“The main result (reported in our paper) was a proof that it is not possible to efficiently solve a certain mathematical problem – specifically checking the convexity of a polynomial, assuming that P is not NP, which is a widely believed conjecture in the field,” Olshevsky explained. “The problem itself is a simplified version of some of the more sophisticated approximation questions that often appear in optimization and control theory, so our paper appears to have a very pessimistic message at the moment. However, we hope that figuring out which problems are un-solvable will be extremely helpful in finding solvable subcases to be used for modeling real systems.”
Olshevsky joined the Illinois faculty in 2012, having previously worked at Princeton University and Los Alamos National Laboratory. He received a PhD in electrical engineering and computer science from MIT in September 2010. Prior to that, he received a BS in applied mathematics and a BS in electrical engineering from Georgia Tech, both in 2004.
His research interests are in control theory, optimization, and applied probability. He is currently interested in the design of distributed control policies which allow large networks of agents (such as formations of vehicles, mobile sensors, or the nodes in a communication network) to function reliably in uncertain and rapidly changing environments. ___________________
Contact:Alexander Olshevsky, Department of Industrial and Enterprise Systems Engineering, 217/333-0329.
If you have any questions about the College of Engineering, or other story ideas, contact Rick Kubetz, writer/editor, Engineering Communications Office, University of Illinois at Urbana-Champaign, 217/244-7716.