Inexact direct-search methods for bilevel optimization problems
本文提出新的直接搜索方法求解双层优化问题，利用固定精度的黑箱求解下层问题，处理光滑和非光滑目标，给出收敛性保证和复杂度界，数值实验验证了有效性。
Abstract In this work, we introduce new direct-search schemes for the solution of bilevel optimization (BO) problems. Our methods rely on a fixed accuracy blackbox oracle for the lower-level problem, and deal both with smooth and potentially nonsmooth true objectives. We thus analyze for the first time in the literature direct-search schemes in these settings, giving convergence guarantees to approximate stationary points, as well as complexity bounds in the smooth case. We also propose the first adaptation of mesh adaptive direct-search schemes for BO. Some preliminary numerical results on a standard set of bilevel optimization problems show the effectiveness of our new approaches.