Upcoming talks

• November 16th 2026, 11:30 p.m. Room TBD Centro Didattico Morgagni, Andrea Cristofari (Associate Professor Università di Roma "Tor Vergata")  

Title: Block cubic Newton with greedy selection

Abstract: In this talk, a second-order block coordinate descent method is described for the unconstrained minimization of an objective function with a Lipschitz continuous Hessian. In the proposed scheme, a greedy (Gauss-Southwell) rule is employed for the block selection, without requiring any predetermined structure, while a cubic model is used for the block update. Global convergence to stationary points is discussed for non-convex objective functions, together with a worst-case iteration complexity analysis. In particular, given a tolerance ε, at most O(ε^(−3/2)) iterations are needed to drive the stationarity violation with respect to a selected block of variables below ε, while at most O(ε^(−2)) iterations are needed to drive the stationarity violation with respect to all variables below ε. Numerical results are also shown, comparing the proposed approach with other second-order methods and block selection rules. Finally, some aspects of the proposed scheme are discussed, including its differences from other approaches and some open questions.