# ε-Subgradient Algorithms for Bilevel Convex Optimization

arXiv: https://arxiv.org/abs/1703.02648 · HTML: https://mlsanity.com/paper/1703.02648/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Mar 2017.

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

- [Convex Bi-Level Optimization Problems with Non-smooth Outer Objective Function](https://mlsanity.com/paper/2307.08245/) (2023)
- [An Accelerated Gradient Method for Convex Smooth Simple Bilevel Optimization](https://mlsanity.com/paper/2402.08097/) (2024)
- [Functionally Constrained Algorithm Solves Convex Simple Bilevel Problems](https://mlsanity.com/paper/2409.06530/) (2024)

## Abstract (arXiv)

This paper introduces and studies the convergence properties of a new class of explicit ε-subgradient methods for the task of minimizing a convex function over the set of minimizers of another convex minimization problem. The general algorithm specializes to some important cases, such as first-order methods applied to a varying objective function, which have computationally cheap iterations. We present numerical experimentation regarding certain applications where the theoretical framework encompasses efficient algorithmic techniques, enabling the use of the resulting methods to solve very large practical problems arising in tomographic image reconstruction.