An inertial extrapolation method for convex simple bilevel optimization

TL;DR

This paper introduces an inertial extrapolation method for convex simple bilevel optimization problems, demonstrating improved convergence and performance over existing algorithms through theoretical analysis and numerical experiments.

Contribution

The paper proposes a novel fixed-point iterative method with inertial extrapolation for convex simple bilevel problems, establishing its convergence and superior efficiency.

Findings

The proposed method converges under standard assumptions.

Numerical results show it outperforms existing algorithms.

The approach effectively handles smooth and nonsmooth inner problems.

Abstract

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.