Dual approaches to the strongly convex simple function minimization problem under affine restrictions

TL;DR

This paper develops dual approaches for strongly convex optimization problems with affine restrictions, utilizing the primal-dual structure and Fast Gradient Method to efficiently find solutions.

Contribution

It introduces a dual problem formulation and a primal-dual solution construction method applicable to a wide range of optimization algorithms.

Findings

Effective dual problem formulation for strongly convex functions

Primal-dual method leveraging Fast Gradient Method

Generalization of techniques to various optimization methods

Abstract

We consider strongly convex optimization problems with affine-type restrictions. We build dual problem and solve dual problem by Fast Gradient Method. We use primal-dual structure of this method to construct the solution of the primal problem. The paper contain a lot of different tricks that allows to generalize mentioned above results for almost all methods we would like to choose to solve the dual problem.