Convex Synthesis of First-Order Methods for Time-Varying Smooth Strongly Convex Optimization

Abstract

Time-varying optimization is fundamental to decision-making in dynamic environments, where objectives evolve over time due to exogenous signals or data streams. However, algorithms designed for static problems yield suboptimal decisions in dynamic scenarios, even asymptotically. In this paper, we develop a robust control synthesis framework to systematically design first-order methods for smooth strongly convex problems that vary in time. Our approach leverages both convex robust control synthesis in the static setting and the internal model principle by directly embedding a model of the underlying variability into the designed algorithm.