6 papers
Convex Synthesis of First-Order Methods for Time-Varying Smooth Strongly Convex Optimization
Bryan Van Scoy, Gianluca Bianchin
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…
The Speed-Robustness Trade-Off for First-Order Methods with Additive Gradient Noise
Bryan Van Scoy, Laurent Lessard
We study the trade-off between convergence rate and sensitivity to stochastic additive gradient noise for first-order optimization methods. Ordinary Gradient Descent (GD) can be ma…
The Internal Model Principle of Time-Varying Optimization
Gianluca Bianchin, Bryan Van Scoy
Time-varying optimization problems are central to many engineering applications, where performance metrics and system constraints evolve dynamically with time. Several algorithms h…
Temporal Variabilities Limit Convergence Rates in Gradient-Based Online Optimization
Bryan Van Scoy, Gianluca Bianchin
This paper investigates the fundamental performance limits of gradient-based algorithms for time-varying optimization. Leveraging the internal model principle and root locus techni…
Feedback Optimization of Dynamical Systems in Time-Varying Environments: An Internal Model Principle Approach
Gianluca Bianchin, Bryan Van Scoy
Feedback optimization has emerged as a promising approach for regulating dynamical systems to optimal steady states that are implicitly defined by underlying optimization problems.…
The Fastest Known First-Order Method for Minimizing Twice Continuously Differentiable Smooth Strongly Convex Functions
Bryan Van Scoy, Laurent Lessard
We consider iterative gradient-based optimization algorithms applied to functions that are smooth and strongly convex. The fastest globally convergent algorithm for this class of f…