On the convergence rate of the boosted Difference-of-Convex Algorithm (DCA)

This code allows reproducing the results from (arXiv):

[1] Hadi Abbaszadehpeivasti, Etienne de Klerk, Adrien Taylor (2025). "On the convergence rate of the boosted Difference-of-Convex Algorithm (DCA)."

Requirements:

• Files in the PEPit folder relies on Python and requires the installation of PEPit.
• Files in the PESTO folder relies on Matlab and requires the installation of PESTO.

Codes

(1) Execution in Python (requires installation of PEPit)

• Boosted_DCA.ipynb: full jupyter notebook to re-obtain the numerical study (and comparison with the rates provided in [1]) of the boosted DCA algorithm. The scripts also allow direct study of the algorithms under Lojasiewicz-type properties.
• Gradient_descent.ipynb: full jupyter notebook to re-obtain the numerical study (and comparison with the rates provided in [1]) of gradient descent applied to a smooth function satisfying a Lojasiewicz-type property.

(2) Execution in Matlab (requires installation of PESTO)

• Boosted_DCA_script.m: main script (calling other functions) that allows numerical study (and comparison with the rates provided in [1]) and to reproduce Figure 1, Figure 2, and Figure 3 of [1].
• Boosted_DCA.m: PESTO code to perform the worst-case analysis of boosted DCA.
• Shifted_minimization.m: helper function that allows simpler implementation of the boosted DCA within the PESTO framework.

(3) One-iteration analysis

• Boosted_DCA_script.m: Mathematica notebook for verifying the reformulations (computer-algebra version).
• Boosted_DCA_script.m: Jupyter notebook for verifying the reformulations (numerical version, with PEPit).