Iteration complexity of the Difference-of-Convex Algorithm for unconstrained optimization: a simple proof
Optimization and Control
2026-01-23 v1
Abstract
We propose a simple proof of the worst-case iteration complexity for the Difference of Convex functions Algorithm (DCA) for unconstrained minimization, showing that the global rate of convergence of the norm of the objective function's gradients at the iterates converge to zero like o(1/k). A small example is also provided indicating that the rate cannot be improved.
Cite
@article{arxiv.2601.15970,
title = {Iteration complexity of the Difference-of-Convex Algorithm for unconstrained optimization: a simple proof},
author = {Serge Gratton and Philippe L. Toint},
journal= {arXiv preprint arXiv:2601.15970},
year = {2026}
}