4 papers
First-Order Analysis of Optimization in Uniformly Convex Metric Spaces: Directional Subderivatives and Basic Descent
D. Russell Luke, Titus Pinta, Qinyu Yan
We develop tools for the analysis and implementation of explicit first-order methods for minimizing functions in uniformly convex metric spaces. We formulate sufficient conditions…
A Newton-Kantorovich Inverse Function Theorem in Quasi-Metric Spaces
Titus Pinta
The purpose of this work is to investigate root finding problems defined on (quasi-)metric spaces, and ranging in Euclidean spaces. The motivation for this line of inquiry stems fr…
A Newton-type Method for Non-smooth Under-determined Systems of Equations
Titus Pinta
We study a variant of Newton's algorithm applied to under-determined systems of non-smooth equations. The notion of regularity employed in our work is based on Newton differentiabi…
A Stochastic Newton-type Method for Non-smooth Optimization
Titus Pinta
We introduce a new framework for analyzing (Quasi-}Newton type methods applied to non-smooth optimization problems. The source of randomness comes from the evaluation of the (appro…