13 papers · 1 filter
Primal-dual multigrid methods for nonsmooth optimization
Felipe Guerra, Tuomo Valkonen
In optimization, one often encounters problems of the form . In this work, we combine primal-dual algorithms with multigrid techniques for their solution. T…
Single-loop approaches to nonsmooth bilevel optimisation
Ensio Suonperä, Tuomo Valkonen
We study bilevel optimisation problems in which the inner problem is represented as a set-valued, parametric constraint. We develop relevant optimistic and pessimistic calculus rul…
Dynamic inverse problems: Single-loop online algorithms
Jyrki Jauhiainen, Yassine Nabou, Tuomo Valkonen
We study efficient online methods for dynamic inverse problems with infinite time horizon. We concentrate, in particular, on problems whose forward model arises from a PDE. Our mot…
Introduction to Nonsmooth Analysis and Optimization
Christian Clason, Tuomo Valkonen
Functions that are not differentiable in the classical sense have become a central tool in modern mathematical models for imaging, inverse problems, machine learning, and optimal c…
Forward-backward splitting in bilaterally bounded Alexandrov spaces
Heikki von Koch, Tuomo Valkonen
With the goal of solving optimisation problems on non-Riemannian manifolds, such as geometrical surfaces with sharp edges, we develop and prove the convergence of a forward-backwar…
Differential estimates for fast first-order multilevel nonconvex optimisation
Neil Dizon, Tuomo Valkonen
With a view on bilevel and PDE-constrained optimisation, we develop iterative estimates of for composite functions , where is the…