An inertial extrapolation method for convex simple bilevel optimization. (2nd January 2021) - Shehu, Yekini; Vuong, Phan Tu; Zemkoho, Alain
ABSTRACT: We consider a scalar objective minimization problem over the solution set of another optimization problem. This problem is known as a 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 non-smooth functions while the outer one is the minimization of a smooth convex function. We first formulate and give strong convergence analysis of an inertial algorithm for fixed-point problem of a non-expansive operator in an infinite dimensional Hilbert space. Then we convert the simple bilevel optimization problem to a fixed-point problem of a non-expansive operator in finite dimensional space and design the corresponding algorithm and establish its convergence. Our numerical experiments show that the proposed method in this paper outperforms the currently known best algorithm to solve the class of bilevel optimization problem considered.