Title: first-order methods for convex programs with functional constraints

Speaker: Prof. Xu Yangyang, Rensselaer Polytechnic Institute, US

Abstract: First-order methods use gradient and/or function value information. They are generally much cheaper than second or higher-order methods. Recently, first-order methods have been popularly used in applications such as machine learning and image processing. These applications are often unconstrained or only have affinely constraints.

In this talk, I will present first-order methods on solving problems with nonlinear functional constraints. In the first part, I will give a deterministic first-order method that is based on linearizing the classic augmented Lagrangian function, and in the second part, I will give its two stochastic versions. Theoretical convergence rate and also numerical results will be presented.