The Multi-Block DC Function Class: Theory, Algorithms, and Applications

ICLR 2026 Conference Submission20060 Authors

Keywords: Multi-block DC, DC programming, non-convex optimization

TL;DR: This work proposes and studies the broad class of multi-block DC functions with many applications.

Abstract: We present the Multi-Block DC (BDC) class, a broad class of structured nonconvex functions that admit a DC (“difference-of-convex”) decomposition across parameter blocks. This block structure not only subsumes the usual DC programming, it turns out to be provably more powerful. Specifically, we demonstrate how standard models (e.g., polynomials and tensor factorization) must have DC decompositions of exponential size, while their BDC formulation is polynomial. This separation in complexity also underscores another key aspect: unlike DC formulations, obtaining BDC formulations for problems is vastly easier and constructive. We illustrate this aspect by presenting explicit BDC formulations for modern tasks such as deep ReLU networks, a result with no known equivalent in the DC class. Moreover, we complement the theory by developing algorithms with non-asymptotic convergence theory, including both batch and stochastic settings, and illustrate their empirical performance through several experiments.

Primary Area: optimization

Submission Number: 20060