Continuous Optimization Seminar - Naomi Graham

Title: Introduction to Monotone Operators

Abstract: 

This talk will be an entry level introduction to the theory of monotone operators as they are presented in Bauschke and Combette’s Convex Analysis and Monotone Operator Theory in Hilbert Spaces. We will discuss maximally monotone operators and their connection to resolvents as well as fixed points of nonexpansive operators. We will see that some classical optimization algorithms can be formulated as iteratively approximating the fixed points of the resolvent of some maximally monotone operator.