# Prediction-Correction Algorithms for Time-Varying Constrained Optimization

arXiv: https://arxiv.org/abs/1611.03681 · HTML: https://mlsanity.com/paper/1611.03681/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Nov 2016.

## Built on by (most cited first, 6 of 6)

- [Predictor-corrector algorithms for stochastic optimization under gradual distribution shift](https://mlsanity.com/paper/2205.13575/) (2022)
- [Online Graph Learning in Dynamic Environments](https://mlsanity.com/paper/2110.05023/) (2021)
- [A Novel Theoretical Framework for Exponential Smoothing](https://mlsanity.com/paper/2403.04345/) (2024)
- [Prediction techniques for dynamic imaging with online primal-dual methods](https://mlsanity.com/paper/2405.02497/) (2024)
- [Online Graph Filtering Over Expanding Graphs](https://mlsanity.com/paper/2409.07204/) (2024)
- [Distributed Optimization with Streaming Data: A Temporal Weighting Perspective](https://mlsanity.com/paper/2608.09565/) (2026)

## Abstract (arXiv)

This paper develops online algorithms to track solutions of time-varying constrained optimization problems. Particularly, resembling workhorse Kalman filtering-based approaches for dynamical systems, the proposed methods involve prediction-correction steps to provably track the trajectory of the optimal solutions of time-varying convex problems. The merits of existing prediction-correction methods have been shown for unconstrained problems and for setups where computing the inverse of the Hessian of the cost function is computationally affordable. This paper addresses the limitations of existing methods by tackling constrained problems and by designing first-order prediction steps that rely on the Hessian of the cost function (and do not require the computation of its inverse). In addition, the proposed methods are shown to improve the convergence speed of existing prediction-correction methods when applied to unconstrained problems. Numerical simulations corroborate the analytical results and showcase performance and benefits of the proposed algorithms. A realistic application of the proposed method to real-time control of energy resources is presented.