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An inertial extrapolation method for convex simple bilevel optimization

Yekini Shehu(yekini.shehu***at***unn.edu.ng)
Phan Tu Vuong(vuong.phan***at***univie.ac.at)
Alain Zemkoho(a.b.zemkoho***at***soton.ac.uk)

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.

Keywords: simple bilevel optimization, fixed-point iterative method, inertial extrapolation

Category 1: Convex and Nonsmooth Optimization

Category 2: Nonlinear Optimization (Constrained Nonlinear Optimization )

Citation:

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Entry Submitted: 09/17/2018
Entry Accepted: 09/17/2018
Entry Last Modified: 09/17/2018

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