# Prediction-Correction Interior-Point Method for Time-Varying Convex Optimization

arXiv: https://arxiv.org/abs/1608.07544 · HTML: https://mlsanity.com/paper/1608.07544/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Aug 2016.

## Built on by (most cited first, 8 of 8)

- [Predictor-corrector algorithms for stochastic optimization under gradual distribution shift](https://mlsanity.com/paper/2205.13575/) (2022)
- [First-Order Dynamic Optimization for Streaming Convex Costs](https://mlsanity.com/paper/2310.07925/) (2023)
- [Safe Gradient Flow for Bilevel Optimization](https://mlsanity.com/paper/2501.16520/) (2025)
- [Augmented Lagrangian Methods for Time-varying Constrained Online Convex Optimization](https://mlsanity.com/paper/2205.09571/) (2022)
- [Distributed Unconstrained Optimization with Time-varying Cost Functions](https://mlsanity.com/paper/2212.09472/) (2022)
- [Time-Varying Convex Optimization with O(n) Computational Complexity](https://mlsanity.com/paper/2410.15009/) (2024)
- [Optimal Parameter Adaptation for Safety-Critical Control via Safe Barrier Bayesian Optimization](https://mlsanity.com/paper/2503.19349/) (2025)
- [Distributed Optimization with Streaming Data: A Temporal Weighting Perspective](https://mlsanity.com/paper/2608.09565/) (2026)

## Abstract (arXiv)

In this paper, we develop an interior-point method for solving a class of convex optimization problems with time-varying objective and constraint functions. Using log-barrier penalty functions, we propose a continuous-time dynamical system for tracking the (time-varying) optimal solution with an asymptotically vanishing error. This dynamical system is composed of two terms: (i) a correction term consisting of a continuous-time version of Newton's method, and (ii) a prediction term able to track the drift of the optimal solution by taking into account the time-varying nature of the objective and constraint functions. Using appropriately chosen time-varying slack and barrier parameters, we ensure that the solution to this dynamical system globally asymptotically converges to the optimal solution at an exponential rate. We illustrate the applicability of the proposed method in two practical applications: a sparsity promoting least squares problem and a collision-free robot navigation problem.