Local convergence of Newton’s method in the classical calculus of variations

Authors

Mark Gockenbach, Michigan Technological UniversityFollow
Chang Liu, Michigan Technological University

Document Type

Article

Publication Date

6-28-2013

Abstract

Sufficient conditions for a weak local minimizer in the classical calculus of variations can be expressed without reference to conjugate points. The local quadratic convergence of Newton’s method follows from these sufficient conditions. Newton’s method is applied in the minimization form; that is, the step is generated by minimizing the local quadratic approximation. This allows the extension to a globally convergent line search based algorithm (which will be presented in a future paper).

Publisher's Statement

Publisher's version of record: https://doi.org/10.1080/02331934.2013.811664

Publication Title

Optimization

Recommended Citation

Gockenbach, M., & Liu, C. (2013). Local convergence of Newton’s method in the classical calculus of variations. Optimization, 64(4). http://doi.org/10.1080/02331934.2013.811664
Retrieved from: https://digitalcommons.mtu.edu/math-fp/13