On the Composition of Two Linear Projections

Abstract: Projection operators are fundamental algorithmic operators in Analysis and Optimization. It is well known that these operators are firmly nonexpansive; however, their composition is generally only averaged and no longer firmly nonexpansive. We will introduce the modulus of averagedness and provide an exact result for the composition of two linear projection operators. As a consequence, we deduce that the Ogura-Yamada bound for the modulus of the composition is sharp. Based on joint work with Theo Bendit and Walaa Moursi.

Mathematics

Audience: researchers in the topic

PIMS-CORDS SFU Operations Research Seminar