University of Minnesota
Aerospace Engineering and Mechanics
Winter 1999 Seminar Series

The Interior-point Revolution in Large-Scale Optimization - Applications in Multi-Aircraft Conflict Resolution

Dr. Vipin Gopal

Principal Research Scientist

Honeywell Technology Center


The last decade has witnessed tremendous amount of research activity in the theory and application of interior point methods for optimization. In linear programming, the publication of a polynomial time algorithm by Karmarkar in 1984 signaled the birth of the class of algorithms called 'interior point methods' and has seen significant advancements since then. The applicability of interior point methods for the solution of nonlinear programming has also been of interest, and recent publications have shown huge potential benefits. The first part of this talk will briefly outline the developments in interior point methods for large-scale linear and nonlinear programming. Conflict detection and resolution (CDR) of multiple aircrafts, a key element in the concept of free flight, will be discussed as an application area. The many-on-many resolution problem pose interesting challenges, as the number of conflict avoidance constraints, which are inequalities, grow polynomially with the number of aircrafts. Here we see that algorithms based on interior point methods show improved performances over methods based on active sets for problems which are highly 'inequality-constrained'. Results for upto four aircrafts will be presented.

Friday, February 19, 1999
209 Akerman Hall
2:30-3:30 p.m.

Refreshments served after the seminar in 227 Akerman Hall.
Disability accomodations provided upon request.
Contact Kristal Belisle, Senior Secretary, 625-8000.