3 papers
math.OC2026
A nonmonotone extrapolated proximal gradient-subgradient algorithm beyond global Lipschitz gradient continuity
Lei Yang, Jingjing Hu, Tianxiang Liu
With the advancement of modern applications, an increasing number of composite optimization problems arise whose smooth component does not possess a globally Lipschitz continuous g…
math.OC2026
Concrete convergence rates for common fixed point problems under Karamata regularity
Tianxiang Liu, Bruno F. Lourenço
We introduce the notion of Karamata regular operators, which is a notion of regularity that is suitable for obtaining concrete convergence rates for common fixed point problems. Th…
math.OC2025
On the equivalence of a Hessian-free inequality and Lipschitz continuous Hessian
Radu I. Boţ, Minh N. Dao, Tianxiang Liu +2
It is known that if a twice differentiable function has a Lipschitz continuous Hessian, then its gradients satisfy a Jensen-type inequality. In particular, this inequality is Hessi…