# Time-Varying Convex Optimization via Time-Varying Averaged Operators

arXiv: https://arxiv.org/abs/1704.07338 · HTML: https://mlsanity.com/paper/1704.07338/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Apr 2017.

## Built on by (most cited first, 3 of 3)

- [Wide and Deep Graph Neural Network with Distributed Online Learning](https://mlsanity.com/paper/2107.09203/) (2021)
- [Optimization in Open Networks via Dual Averaging](https://mlsanity.com/paper/2105.13348/) (2021)
- [OpReg-Boost: Learning to Accelerate Online Algorithms with Operator Regression](https://mlsanity.com/paper/2105.13271/) (2021)

## Abstract (arXiv)

Devising efficient algorithms that track the optimizers of continuously varying convex optimization problems is key in many applications. A possible strategy is to sample the time-varying problem at constant rate and solve the resulting time-invariant problem. This can be too computationally burdensome in many scenarios. An alternative strategy is to set up an iterative algorithm that generates a sequence of approximate optimizers, which are refined every time a new sampled time-invariant problem is available by one iteration of the algorithm. These types of algorithms are called running. A major limitation of current running algorithms is their key assumption of strong convexity and strong smoothness of the time-varying convex function. In addition, constraints are only handled in simple cases. This limits the current capability for running algorithms to tackle relevant problems, such as ℓ1-regularized optimization programs. In this paper, these assumptions are lifted by leveraging averaged operator theory and a fairly comprehensive framework for time-varying convex optimization is presented. In doing so, new results characterizing the convergence of running versions of a number of widely used algorithms are derived.