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.
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.
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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.