# $\epsilon$-Subgradient Algorithms for Bilevel Convex Optimization

## TL;DR

This paper develops and analyzes a new class of explicit $psilon$-subgradient algorithms for bilevel convex optimization, demonstrating their effectiveness in large-scale practical problems like tomographic image reconstruction.

## Contribution

It introduces a novel $psilon$-subgradient method with proven convergence for bilevel convex problems, applicable to large-scale applications.

## Key findings

- Effective in solving large-scale problems
- Convergence properties established
- Applicable to tomographic image reconstruction

## Abstract

This paper introduces and studies the convergence properties of a new class of explicit $\epsilon$-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.