Stochastic First-order Methods for Convex and Nonconvex Functional Constrained Optimization. (arXiv:1908.02734v4 [math.OC] UPDATED)

Web: http://arxiv.org/abs/1908.02734

Functional constrained optimization is becoming more and more important in
machine learning and operations research. Such problems have potential
applications in risk-averse machine learning, semisupervised learning, and
robust optimization among others. In this paper, we first present a novel
Constraint Extrapolation (ConEx) method for solving convex functional
constrained problems, which utilizes linear approximations of the constraint
functions to define the extrapolation (or acceleration) step. We show that this
method is a unified algorithm that achieves the best-known rate of convergence …

arxiv math optimization stochastic