A Self-adaptive Algorithm with Multi-step Inertia for Solving Convex Bilevel Optimization Problems

In this paper, we propose an adaptive algorithm with multi-step inertia for solving a convex bilevel optimization problem. Under suitable parameter conditions, we prove that our algorithm converges strongly to some solution of the problem, which is the unique solution of some variational inequality problem. The effectiveness of the proposed algorithm is verified by numerical experiments and compared with other algorithms. 2010 Mathematics Subject Classification 47H09, 47H10, 65K10, 90C25.