Algorithm Library

Linnaeus includes an algorithm library to serve as a reference. Users can check the potential relations between the input algorithm and reference algorithms in the library. The algorithms can be accessed through name abbreviations. Currently, the algorithm library includes:

• Gradient descent method, accessed by Gr
• Nesterov's accelerated gradient method, accessed by Ng
• Heavy-ball method, accessed by Hb
• Triple momentum algorithm, accessed by Tm
• Proximal point method, accessed by Pp
• Proximal point method with relaxation, accessed by Pp_r
• Proximal gradient method, accessed by Pg
• Douglas-Rachford splitting, accessed by Dr
• Permutation of Douglas-Rachford splitting, accessed by Dr_p
• Peaceman-Rachford splitting method, accessed by Pr
• Alternating direction method of multipliers (ADMM), accessed by Admm
• Chambolle-Pock method, accessed by Cp
• Davis-Yin splitting method, accessed by Dy
• Extragradient method, accessed by Eg
• Extragradient method by Korpelevich and Antipin, accessed by Eg_ka
• Extragradient method by Tseng, accessed by Eg_t
• Reflected gradient method by Malitsky, accessed by Rg

The whole library is accessed by algo_library.library.

The following code checks equivalence between Gradient descent method and Triple momentum method in the library.

import linnaeus as lin
lin.is_equivalent(lin.Gr, lin.Tm)

The results are the same as the previous example.

Further, the next example checks equivalence of Gradient descent method among all the algorithms in the library.

lin.is_equivalent(lin.Gr, lin.algo_library.library)