A First-order Prediction-Correction Algorithm for Time-varying (Constrained) Optimization

This paper focuses on the design of online algorithms based on prediction-correction steps to track the optimal solution of a time-varying constrained problem. Existing prediction-correction methods have been shown to work well for unconstrained convex problems and for settings where obtaining the inverse of the Hessian of the cost function can be computationally affordable. The prediction-correction algorithm proposed in this paper addresses the limitations of existing methods by tackling constrained problems and by designing a first-order prediction step that relies on the Hessian of the cost function. Analytical results are established to quantify the tracking error. Numerical simulations corroborate the analytical results and showcase the performance and benefits of the algorithms.