ECE Seminar: Rapidly Converging Active-Set Methods for Convex Quadratic Programming
Friday, April 5, 2013 - 11:45am to 1:00pm
Daniel Robinson, Ph.D., Assistant Professor, Department of Applied Mathematics and Statistics, Johns Hopkins University
I present two algorithms designed to solve large-scale quadratic programs. Both algorithms are of the active-set variety, allow rapid adjustment of active-set estimates, compute highly accurate solutions, and effectively utilize a good initial estimate of a solution (when available). The first algorithm rapidly identifies constraints active at a solution via the use of matrix splitting iterations. Our experience shows that this is a more effective identification procedure than the simpler projected gradient strategy that is commonly used. Additional acceleration of the iterates to a solution is obtained by using subspace steps for which iterative linear system methods such as the conjugate gradient method may be used. The second algorithm extends recent work by Hintermuller, Ito, and Kunisch for solving problems with very specific structure associated with certain discretized PDE constrained optimization problems, to more general convex problems. This generalization is achieved via the introduction of an auxiliary index set that houses those variables that may lead to cycling (failure). Preliminary numerical results are given for both methods. Bio: Daniel Robinson received his Ph.D. in 2007 from the University of California, San Diego, under his supervisor Philip E. Gill. He is currently an Assistant Professor at Johns Hopkins University in the Department of Applied Mathematics and Statistics in the Whiting School of Engineering.