OS Numerical Optimization: On the nonmonotone forward-backward splitting method for solving a class of nonsmooth composite problems
Dienstag, 13. Juni 2023
15:15 bis 16:45 Uhr
B. Azmi & S. Volkwein
Vortragende Person/Vortragende Personen:
On 13th June 2023 at 15:15, Marco Bernreuther from the University of Konstanz will give a talk.
This talk provides a comprehensive study of the nonmonotone forward-
backward splitting (FBS) method for solving a class of nonsmooth
composite problems in Hilbert spaces. The objective function is the
sum of a Fréchet differentiable (not necessarily convex) function and
a proper lower semicontinuous convex (not necessarily smooth)
function. These problems appear, for example, frequently in the context
of optimal control of nonlinear partial differential equations (PDEs)
with nonsmooth sparsity promoting cost functionals. We discuss the
convergence and complexity of FBS equipped with the nonmonotone
linesearch under different conditions. In particular, R-linear convergence
will be derived under quadratic growth-type conditions. We also investigate
the applicability of the algorithm to problems governed by PDEs.
Numerical experiments are also given that justify our theoretical findings.
At the end of the talk, open research questions and a related
switching problem will be shortly discussed.