Combining approximation and exact penalty in hierarchical programming. (3rd August 2022)

• Record Type: Journal Article
• Authors: Bigi, Giancarlo; Lampariello, Lorenzo; Sagratella, Simone
• Is Part Of: Optimization. Volume 71:Number 8(2022)
• Page Start: 2403
• Page End: 2419
• Publication Date: 2022-08-03
• Subjects: Hierarchical programming -- optimization problems with variational inequality constraints -- approximation approaches -- penalty techniques; 65K10 -- 90C30 -- 90C33 -- 90C25 -- 65K15; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2021.1939336
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : We address the minimization of an objective function over the solution set of a (non-parametric) lower-level variational inequality. This problem is a special instance of semi-infinite programs and encompasses, as particular cases, simple (smooth) bilevel and equilibrium selection problems. We resort to a suitable approximated version of the hierarchical problem. We show that this, on the one hand, does not perturb the original (exact) program 'too much', on the other hand, allows one to rely on some suitable exact penalty approaches whose convergence properties are established.