Random constraint sampling and duality for convex optimization

TL;DR

This paper introduces a combined approach of random constraint sampling with primal-dual algorithms to efficiently solve large-scale convex optimization problems, providing convergence analysis and numerical validation.

Contribution

It presents a novel integration of random sampling with primal-dual methods for convex optimization, along with convergence rate analysis and empirical results.

Findings

The combined algorithm converges at a quantifiable rate.

Numerical experiments demonstrate the method's effectiveness.

Approach scales well with problem size.

Abstract

We are interested in solving convex optimization problems with large numbers of constraints. Randomized algorithms, such as random constraint sampling, have been very successful in giving nearly optimal solutions to such problems. In this paper, we combine random constraint sampling with the classical primal-dual algorithm for convex optimization problems with large numbers of constraints, and we give a convergence rate analysis. We then report numerical experiments that verify the effectiveness of this algorithm.