A First Order Method for Solving Convex Bilevel Optimization Problems
研究内层最小化光滑与非光滑函数之和、外层在最优解集上最小化光滑强凸函数的凸双层优化问题，分析基于不动点算法的一阶方法，建立内层目标函数值的全局次线性收敛速度。
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.