Mirror Descent Methods for Quasar Convex Optimization Problems With Non-Smooth Inequality Constraints

In this paper, we consider constraint optimization problems subject to non-smooth convex functional (inequality-type) constraints, wherein the objective function is non-smooth and quasar convex. We propose and analyze two groups of algorithms, each consisting of a standard version and a modified variant, that operate by switching between two types of iteration points: productive and non-productive. Within each group, we develop distinct mirror descent-type algorithms for both deterministic and stochastic settings, and we establish their convergence rates.