A First Order Method for Solving Convex Bilevel Optimization Problems
Shoham Sabach, Shimrit Shtern · SIAM Journal on Optimization · 2017
In this paper we study convex bilevel optimization problems for which the inner level consists of minimization of the sum of smooth and nonsmooth functions. The outer level aims at minimizing a smooth and strongly convex function over the optimal solutions set of the inner problem. We analyze a first order method which is based on an existing fixed-point algorithm. Global sublinear rate of convergence of the method is established in terms of the inner objective function values.