Education is not the filling of a pail, it is the lighting of a fire. - W. B. Yeats

 

NEWS in the Department of Mathematics
Graduate Announcements

 

Brent Davis - PhD defense
Date:  Wednesday, May 24, 2017
Place:  Weber 201
Time:  9:00 a.m.

Title:  The numerical algebraic geometry approach to polynomial optimization

Advisor:  Dr. Dan Bates   Co-Advisor:  Dr. Chris Peterson

Committee:  Dr. Michael Kirby,  Dr. Anthony Maciejewski

Abstract:  Numerical algebraic geometry (NAG) consists of a collection of numerical algorithms based on homotopy continuation to approximate the solution set of systems of polynomial equations arising from applications in science and engineering. This research focused on finding global solutions to constrained polynomial optimization problems of moderate size using NAG methods. The benefit of employing a NAG approach to nonlinear optimization problems is that every critical point of the objective function is obtained with probability one. The NAG approach to global optimization aims to reduce computational complexity during path tracking by exploiting structure that arises from the corresponding polynomial systems. This thesis will consider applications to systems biology and life sciences where polynomials solve problems in model compatibility, model selection, and parameter estimation. Furthermore, these techniques produce mathematical models of large data sets on non-euclidean manifolds such as a disjoint union of Grassmannians. These methods will also play a role in analyzing the performance of existing local methods for solving polynomial optimization problems.

 







 



 





 

 

 

 

 





nt Davis - PhD defense
Date:  Wednesday, May 24, 2017
Place:  Weber 201
Time:  9:00 a.m.