The role of nonexpansive type mappings in designing fixed point algorithms for Data Science problems
Vasile Berinde
Research Institute for Symbolic Computation
Johannes Kepler Universuty Linz, Austria
ABSTRACT
Various Data Science problems, like regression, classification, or image reconstruction, could be equivalently formulated as optimization problems or variational inequality problems. In order to build iterative schemes for solving the later problems, it is convenient in many instances to transform them into appropriate fixed point problems $x = T(x)$, which naturally generate the Picard fixed point algorithm $x_{n+1}=T (x_n)$, $n\geq 0$. The main aim of this paper is to discuss the role of nonexpansive type mappings $T$ in designing convergent fixed point algorithms with applications to Data Science problems.
SHORT BIO
Temur Kutsia is a senior researcher and associate professor at the Research Institute for Symbolic Computation (RISC) Institute of the Johannes Kepler University Linz, Austria, where he leads a research group on symbolic constraint solving. He obtained his PhD and habilitation from Johannes Kepler University. His research interests lie in computational logic and symbolic artificial intelligence, with a particular focus on equational constraint solving, unification and generalization, as well as rewriting-based deduction and computation. He has authored over 100 publications in these areas, edited 20 conference proceedings and journal special issues, and served on more than 100 program committees of international conferences. He is a member of the IFIP Working Group 1.6 (Term Rewriting) and serves on the editorial board of the Journal of Symbolic Computation.