Year: 2026
Type: preprint
Abstract: We combine CaCuTe with sequential subspace optimization (SESOP) for smooth convex minimization under Lipschitz continuity of the Hessian. The resulting method, CaCuSESOP, achieves the global rate $O(k^{-2})$ with a fixed number of Hessian--vector products per iteration, while removing key limitations of classical SESOP. In particular, exact minimization of the original objective is replaced by minimization of a low-dimensional cubic upper model, which needs only be solved to a computable accuracy. The cubic regularization parameter is selected by backtracking. If the Hessian at the minimizer is positive definite, CaCuSESOP automatically attains an accelerated local linear rate with complexity $O(\sqrt{κ_\star}\log(1/\varepsilon))$. Neither the local strong-convexity parameter, the condition number $κ_\star$, nor the optimal value is supplied to the algorithm. We give finite bounds for entering this regime and adapting the restart schedule. Finally, we prove that the global $O(k^{-2})$ rate is optimal for the considered fixed-budget gradient/Hessian--vector-product linear-span oracle class, even with momentum and unrestricted memory.
Source: arXiv (Cornell University)
Author: Tupitsa, Nazarii
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7220710849