Rank-one inverse updates for the dense Newton system

Develop a bounded sequence of rank-one inverse updates for the fixed-plus-diagonal Newton matrix in the Fast-DeePC BoxQP interior-point method, replacing dense Cholesky factorization to reduce the per-iteration linear-algebra cost from O(n^3) to O(n^2).

Background

The reduced Fast-DeePC problem is a box-constrained quadratic program whose Hessian is generally dense. The proposed implementation factors the Newton matrix, consisting of the constant reduced Hessian plus a changing diagonal barrier term, by dense Cholesky factorization at every interior-point iteration. Although the fixed-plus-diagonal structure could permit a sequence of rank-one inverse updates with lower per-iteration complexity, the paper does not develop or evaluate that alternative.

References

Since \widehat H is constant and only the barrier diagonal varies, the Newton matrix has a fixed-plus-diagonal form. This structure could instead use a bounded sequence of rank-one inverse updates as in , reducing the per-iteration linear-algebra cost from $O(n3)$ to $O(n2)$. We retain dense Cholesky in this work and leave this substitution for future work.

— Fast-DeePC: Fast Data-Enabled Predictive Control using Soft-constrained Scheme  (2610.12902 - Zhang et al., 9 Oct 2026) in Remark 2 ("Dense Newton system"), Section 2.3.3 (subsection "Strong convexity and penalty consistency")