A primal nonsmooth reformulation for bilevel optimization problems

• 成果类型: Article
• 署名作者: Helou, Elias S.; Santos, Sandra A.; Simoes, Lucas E. A.
• 署名单位: Universidade de Sao Paulo; Universidade Estadual de Campinas
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-021-01764-6
• 发表日期: 2023
• 页码: 1381-1409
• 关键词: sampling method; PROGRAMS; gradient; algorithm; nonconvex

摘要

The solution of bilevel optimization problems with possibly nondifferentiable upper objective functions and with smooth and convex lower-level problems is discussed. A new approximate one-level reformulation for the original problem is introduced. An algorithm based on this reformulation is developed that is proven to converge to a solution of the bilevel problem. Each iteration of the algorithm depends on the solution of a nonsmooth optimization problem and its implementation leverages recent advances on nonsmooth optimization algorithms, which are fundamental to obtain a practical method. Experimental work is performed in order to demonstrate some characteristics of the algorithm in practice.