Vector equilibrium problems are a natural generalization to the context of partially ordered spaces of the Ky Fan inequality, where scalar bifunctions are replaced with vector bifunctions. In the present paper, the local geometry of the strong solution set to these problems is investigated through its inner/outer conical approximations. More precisely, formulae for approximating the contingent cone to the set of strong vector equilibria are established, which are expressed via Bouligand derivatives of the bifunctions. These results are subsequently employed for deriving both necessary and sufficient optimality conditions for problems, whose feasible region is the strong solution set to a vector equilibrium problem, so they can be cast in mathematical programming with equilibrium constraints.

Uderzo, A. (2023). First-order approximation of strong vector equilibria with application to nondifferentiable constrained optimization. COMMUNICATIONS IN OPTIMIZATION THEORY, 32, 1-17 [10.23952/cot.2023.32].

First-order approximation of strong vector equilibria with application to nondifferentiable constrained optimization

Uderzo, A
2023

Abstract

Vector equilibrium problems are a natural generalization to the context of partially ordered spaces of the Ky Fan inequality, where scalar bifunctions are replaced with vector bifunctions. In the present paper, the local geometry of the strong solution set to these problems is investigated through its inner/outer conical approximations. More precisely, formulae for approximating the contingent cone to the set of strong vector equilibria are established, which are expressed via Bouligand derivatives of the bifunctions. These results are subsequently employed for deriving both necessary and sufficient optimality conditions for problems, whose feasible region is the strong solution set to a vector equilibrium problem, so they can be cast in mathematical programming with equilibrium constraints.
Articolo in rivista - Articolo scientifico
Contingent cone; Generalized differentiation; Nondifferentiable optimization; Mathematical programming with equilibrium constraint; subdifferential
English
3-lug-2023
2023
32
1
17
partially_open
Uderzo, A. (2023). First-order approximation of strong vector equilibria with application to nondifferentiable constrained optimization. COMMUNICATIONS IN OPTIMIZATION THEORY, 32, 1-17 [10.23952/cot.2023.32].
File in questo prodotto:
File Dimensione Formato  
Uderzo-2023-Com Opt T A-VoR.pdf

Solo gestori archivio

Tipologia di allegato: Publisher’s Version (Version of Record, VoR)
Licenza: Tutti i diritti riservati
Dimensione 406.74 kB
Formato Adobe PDF
406.74 kB Adobe PDF   Visualizza/Apri   Richiedi una copia
Uderzo-2023-Com Opt T A-preprint.pdf

accesso aperto

Tipologia di allegato: Submitted Version (Pre-print)
Licenza: Creative Commons
Dimensione 225.78 kB
Formato Adobe PDF
225.78 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/449058
Citazioni
  • Scopus ND
  • ???jsp.display-item.citation.isi??? ND
Social impact