2025/10/21 by Giancarlo Bigi, Bigi, Giancarlo, Riccardo Tomassini +1
Computer Science · Mathematics · #Advanced Optimization Algorithms Research #Contact Mechanics and Variational Inequalities #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Variational Analysis #math.OC
paper · pdf · doi:10.48550/arxiv.2510.18682
openalex publication_date 2025/10/21 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28 · arxiv created 2026/07/29 · arxiv updated 2026/07/31
A simple bilevel variational problem where the lower level is a variational inequality while the upper level is an optimization problem is studied. We consider an inexact version of the lower problem, which guarantees enough regularity to allow the exploitation of techniques of exact penalization. Moreover, cutting planes are used to approximate the Minty gap function of the lower level. Algorithms to solve the resulting inexact bilevel problem are devised relying on these techniques and approximations. Finally, their convergence is studied in details by analysing also the effect of the given inexactness.