Work

On the convergence rate of the boosted difference-of-convex algorithm (DCA)

Year: 2026

Type: article

Abstract: The difference-of-convex algorithm (DCA) is a well-established nonlinear programming technique that solves successive convex optimization problems. These sub-problems are obtained from the difference-of-convex (DC) decompositions of the objective and constraint functions. We investigate the worst-case performance of the unconstrained DCA, with and without boosting, where boosting simply performs an additional step in the direction generated by the usual DCA method. We show that, for certain classes of DC decompositions, the boosted DCA is provably better in the worst-case than the usual DCA. While several numerical studies have reported that boosted DCA outperforms classical DCA, a theoretical explanation for this behavior has, to the best of our knowledge, not been given until now. Our proof technique relies on semidefinite programming (SDP) performance estimation.

Source: Optimization Letters

DOI: 10.1007/s11590-026-02305-w

Authors: Hadi Abbaszadehpeivasti, Etienne de Klerk, Adrien Taylor

Institutions: Tilburg University, Institut national de recherche en sciences et technologies du numérique

Language: English

Topic: Advanced Optimization Algorithms Research

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funders: European Commission, Agence Nationale de la Recherche, Nederlandse Organisatie voor Wetenschappelijk Onderzoek, European Research Council