Poetry Reading - Poet Laureate of the UP

Russell Thorburn, Poet Laureate of the Upper Peninsula, is visiting Michigan Tech and presenting a reading, workshop, and slide show to the Michigan Tech community from 7 to 8:30 p.m., on Thursday, April 10, in the East Reading room of the Van Pelt and Opie Library. This exceptional event is open to the public and is sponsored by the Friends of the Van Pelt Library; all are welcome and no preregistration is required.

Problems in the classical calculus of variations

This dissertation concerns convergence analysis for nonparametric problems in the calculus of variations and sufficient conditions for weak local minimizer of a functional for both nonparametric and parametric problems. Newton's method in infinite-dimensional space is proved to be well-defined and converges quadratically to a weak local minimizer of a functional subject to certain boundary conditions. Sufficient conditions for global converges are proposed and a well-defined algorithm based on those conditions is presented and proved to converge. Finite element discretization is employed to achieve an implementable line-search-based quasi-Newton algorithm and a proof of convergence of the discretization of the algorithm is included. This work also proposes sufficient conditions for weak local minimizer without using the language of conjugate points. The form of new conditions is consistent with the ones in finite-dimensional case. It is believed that the new form of sufficient conditions will lead to simpler approaches to verify an extremal as local minimizer for well-known problems in calculus of variations.