A Control Theoretical Approach to Online Constrained Optimization

TL;DR

This paper introduces a control theory-based online algorithm for constrained optimization that guarantees asymptotic convergence and effectively handles inequality constraints, outperforming existing methods.

Contribution

It presents a novel control-theoretic online optimization algorithm with convergence guarantees and improved handling of inequality constraints compared to prior approaches.

Findings

Algorithm achieves asymptotic convergence to the optimal trajectory.

Modified algorithm effectively manages wind-up from inequality constraints.

Numerical results show superior performance over state-of-the-art methods.

Abstract

In this paper we focus on the solution of online problems with time-varying, linear equality and inequality constraints. Our approach is to design a novel online algorithm by leveraging the tools of control theory. In particular, for the case of equality constraints only, using robust control we design an online algorithm with asymptotic convergence to the optimal trajectory, differently from the alternatives that achieve non-zero tracking error. When also inequality constraints are present, we show how to modify the proposed algorithm to account for the wind-up induced by the nonnegativity constraints on the dual variables. We report numerical results that corroborate the theoretical analysis, and show how the proposed approach outperforms state-of-the-art algorithms both with equality and inequality constraints.