Oct 25: Daniel Robinson: Matrix splitting methods for bound-constrained quadratic programming and linear complementarity problems

CIS Seminar Series
Tuesday, October 25, 2011
1:00 pm
Clark Hall 314
 
Daniel Robinson, PhD
Assistant Professor
Applied Mathematics and Statistics
JHU
Matrix splitting methods for bound-constrained quadratic programming and linear complementarity problems
I present two-phase matrix splitting methods for solving bound-constrained quadratic programs (BQPs) and linear complementarity problems (LCPs).The method for solving BQPs uses matrix splitting iterations to generate descent directions that drive convergence of the iterates and rapidly identify those variables that are active at the solution. The second-phase uses this prediction to further refine the active set and to accelerate convergence. The method for solving LCP combines matrix splitting iterations with a “natural” merit function..This combination allows one to prove convergence of the method and maintain excellent practical performance. Once again, a second subspace phase is used to accelerate convergence. I present numerical results for both algorithms on CUTEr test problems, randomly generated problems, and the pricing of American options.
Daniel Robinson received his Ph.D. from the Department of Mathematics and Statistics at the University of California, San Diego in 2007. In the summer of 2006, he worked for Northrop Grumman as a consultant with his advisor Philip Gill and developed algorithms for trajectory optimization problems. From 2007-2010, Daniel was a research assistant to Nick Gould at the University of Oxford, England, where he developed and implemented optimization algorithms for large-scale nonlinear and convex optimization. In 2010, Daniel was a postdoctoral fellow for Jorge Nocedalin the Industrial Engineering and Management Sciences Department at Northwestern University. Currently, Daniel is an Assistant Professor at Johns Hopkins University in the Department of Applied Mathematics and Statistics. His current research lies at the interface between Applied Linear Algebra, Operations Research, and Applied Mathematics. In particular, he is interested in the formulation and implementation of efficient algorithms for large-scale continuous optimization, machine learning, and linear complementarity problems

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