# An inertial extrapolation method for convex simple bilevel optimization

arXiv: https://arxiv.org/abs/1809.06250 · HTML: https://mlsanity.com/paper/1809.06250/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Sep 2018.

## Built on by (most cited first, 5 of 5)

- [Investigating Bi-Level Optimization for Learning and Vision from a Unified Perspective: A Survey and Beyond](https://mlsanity.com/paper/2101.11517/) (2021)
- [A Conditional Gradient-based Method for Simple Bilevel Optimization with Convex Lower-level Problem](https://mlsanity.com/paper/2206.08868/) (2022)
- [Projection-Free Methods for Stochastic Simple Bilevel Optimization with Convex Lower-level Problem](https://mlsanity.com/paper/2308.07536/) (2023)
- [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)

## Abstract (arXiv)

We consider a scalar objective minimization problem over the solution set of another optimization problem. This problem is known as simple bilevel optimization problem and has drawn a significant attention in the last few years. Our inner problem consists of minimizing the sum of smooth and nonsmooth functions while the outer one is the minimization of a smooth convex function. We propose and establish the convergence of a fixed-point iterative method with inertial extrapolation to solve the problem. Our numerical experiments show that the method proposed in this paper outperforms the currently best known algorithm to solve the class of problem considered.