Seminar Details
2026-07-02 (10:00) : A two-level inexact smoothing framework for nonsmooth optimization
At Euler building (room A.002)
Duration: 60 minutes
Organized by Mathematical Engineering
Speaker :
Masoud Ahookhosh (University of Antwerp)
Abstract :
We introduce an inexact two-level optimization framework, ItsOPT, for computing first- and second-order critical points of nonsmooth and nonconvex optimization problems. The framework consists of two interconnected levels. At the upper level, a smoothing technique—such as the high-order Moreau envelope, high-order forward-backward envelope, or high-order tensor envelope—is employed to construct a smooth approximation of the original objective function while preserving its minimizers. First- or second-order optimization methods are then applied to minimize the resulting smooth surrogate. At the lower level, the associated high-order proximal subproblems (e.g., high-order proximal, forward-backward, or tensor subproblems) are solved inexactly using subgradient-based or Bregman proximal methods. The resulting approximate solutions provide inexact evaluations of the smoothing function and its derivative information, which are subsequently used by the upper-level optimization methods. The overall complexity of the proposed framework is given by the product of the computational complexities of the upper- and lower-level procedures. By combining accelerated first- or second-order methods at the upper level with lower-level algorithms whose complexity is negligible (e.g., logarithmic in the desired accuracy), the resulting methods may achieve overall iteration complexities that improve upon existing worst-case complexity bounds. Finally, we present several concrete algorithms within the proposed framework and report preliminary numerical results demonstrating their practical performance.