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.

Combining approximation and exact penalty in hierarchical programming / Bigi, G; Lampariello, L; Sagratella, S. - In: OPTIMIZATION. - ISSN 0233-1934. - 71:8(2022), pp. 2403-2419. [10.1080/02331934.2021.1939336]

Combining approximation and exact penalty in hierarchical programming

Sagratella, S
2022

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.
2022
hierarchical programming; optimization problems with variational inequality constraints; approximation approaches; penalty techniques
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Combining approximation and exact penalty in hierarchical programming / Bigi, G; Lampariello, L; Sagratella, S. - In: OPTIMIZATION. - ISSN 0233-1934. - 71:8(2022), pp. 2403-2419. [10.1080/02331934.2021.1939336]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1681854
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