Performance-Estimation-Problems-For-Newton

This code can be used to reproduce the results from the work (on arXiv):

[1] de Klerk, Etienne, Francois Glineur, and Adrien Taylor. "Worst-case convergence analysis of gradient and Newton methods through semidefinite programming performance estimation." SIAM Journal on Optimization 30 (3), 2053-2082, 2020.

Getting started

To use the code, download the repository and execute the files on a one-by-one basis. The code makes use of the Symbolic Computation Toolbox of Matlab.

List of files

• ExactLS_distance_validations Symbolic verification of the worst-case bound (in terms of distance to the optimal solution) obtained when using exact linesearch.

• ExactLS_gradientnorm_validations Symbolic verification of the worst-case bound (in terms of gradient norm) obtained when using exact linesearch.

• Fixedstep_distance_validations_small Symbolic verification of the worst-case bound (in terms of distance to the optimal solution) obtained when using fixed stepsizes.

• Fixedstep_gradientnorm_validations_small Symbolic verification of the worst-case bound (in terms of distance to the optimal solution) obtained when using fixed stepsizes.

• Fixedstep_funcvalues_validations Symbolic verification of the worst-case bound (in terms of objective function accuracy) obtained when using fixed stepsizes.

Authors

• Etienne de Klerk
• François Glineur
• Adrien Taylor