Researchers have developed a new method for minimizing convex functions, called Primal Acceleration of Newton's Method. This approach uses only primal variables and performs one linear solve per iteration, achieving a convergence rate of O(1/k^3) in terms of the functional residual. The method is based on a predetermined choice of parameters and can be implemented in a Hessian-free way using an inexact linear system solver. It also extends to arbitrary geometry through Bregman divergence and composite optimization problems. --- Why it matters: This matters because it provides a new, efficient algorithm for optimizing convex functions, which is a fundamental problem in many areas of machine learning and optimization. The ability to achieve fast convergence rates with minimal computational overhead can have significant impacts on the performance and scalability of AI systems. Source: https://arxiv.org/abs/2608.21359