Self-concordant inclusions: A unified framework for path-following generalized Newton-type algorithms

We study a class of monotone inclusions called “self-concordant inclusion” which covers three fundamental convex optimization formulations as special cases. We develop a new generalized Newton-type framework to solve this inclusion. Our framework subsumes three schemes: full-step, damped-step and path-following methods as specific instances, while allows one to use inexact computation to form generalized Newton … Read more

Generalized Self-Concordant Functions: A Recipe for Newton-type Methods

We study the smooth structure of convex functions by generalizing a powerful concept so-called \textit{self-concordance} introduced by Nesterov and Nemirovskii in the early 1990s to a broader class of convex functions, which we call \textit{generalized self-concordant functions}. This notion allows us to develop a unified framework for designing Newton-type methods to solve convex optimization problems. … Read more