# A Primal-Dual Splitting Algorithm for Finding Zeros of Sums of Maximally Monotone Operators

Radu Ioan Bot^{*}, Ernö Robert Csetnek and Andre Heinrich

We consider the primal problem of finding the zeros of the sum of a maximally monotone operator and the composition of another maximally monotone operator with a linear continuous operator. By formulating its Attouch-Théra-type dual inclusion problem, a primal-dual splitting algorithm which simultaneously solves the two problems is presented. The proposed scheme uses at each iteration separate the resolvents of the maximally monotone operators involved and aims to overcome the shortcoming of classical splitting algorithms when dealing with compositions of maximally monotone and linear continuous operators. The iterative algorithm is used for solving nondifferentiable convex optimization problems arising in image processing and in location theory.

Mathematics Subject Classification: 47H05 65K05 90C25

Keywords: maximally monotone operator; resolvent; operator splitting; subdifferential; duality

Minisymposion: Computational Methods for Inverse Problems/Control Problems in Banach Spaces