Primal-dual stochastic gradient method for convex programs with many functional constraints

Understand

Stochastic gradient method (SGM) has been popularly applied to solve optimization problems with objective that is stochastic or an average of many functions.

• Most existing works on SGMs assume that the underlying problem is unconstrained or has an easy-to-project constraint set.
• In this paper, we consider problems that have a stochastic objective and also many functional constraints.
• For such problems, it could be extremely expensive to project a point to the feasible set, or even compute subgradient and/or function value of all constraint functions.