A global optimization approach for solving non-monotone equilibrium problems (EPs) is proposed. The class of (regularized) gap functions is used to reformulate any EP as a constrained global optimization program and some bounds on the Lipschitz constant of such functions are provided. The proposed global optimization approach is a combination of an improved version of the DIRECT algorithm, which exploits local bounds of the Lipschitz constant of the objective function, with local minimizations. Unlike most existing solution methods for EPs, no monotonicity-type condition is assumed in this paper. Preliminary numerical results on several classes of EPs show the effectiveness of the approach.

Lucidi, S., Passacantando, M., Rinaldi, F. (2022). Solving non-monotone equilibrium problems via a DIRECT-type approach. JOURNAL OF GLOBAL OPTIMIZATION, 83(4), 699-725 [10.1007/s10898-021-01121-z].

Solving non-monotone equilibrium problems via a DIRECT-type approach

Passacantando, M;
2022

Abstract

A global optimization approach for solving non-monotone equilibrium problems (EPs) is proposed. The class of (regularized) gap functions is used to reformulate any EP as a constrained global optimization program and some bounds on the Lipschitz constant of such functions are provided. The proposed global optimization approach is a combination of an improved version of the DIRECT algorithm, which exploits local bounds of the Lipschitz constant of the objective function, with local minimizations. Unlike most existing solution methods for EPs, no monotonicity-type condition is assumed in this paper. Preliminary numerical results on several classes of EPs show the effectiveness of the approach.
No
Articolo in rivista - Articolo scientifico
Scientifica
DIRECT algorithm; Equilibrium problem; Gap function; Global optimization;
English
699
725
27
Lucidi, S., Passacantando, M., Rinaldi, F. (2022). Solving non-monotone equilibrium problems via a DIRECT-type approach. JOURNAL OF GLOBAL OPTIMIZATION, 83(4), 699-725 [10.1007/s10898-021-01121-z].
Lucidi, S; Passacantando, M; Rinaldi, F
File in questo prodotto:
File Dimensione Formato  
SolvingNon-monotoneEPs.pdf

accesso aperto

Descrizione: Article
Tipologia di allegato: Publisher’s Version (Version of Record, VoR)
Dimensione 718.09 kB
Formato Adobe PDF
718.09 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: http://hdl.handle.net/10281/391577
Citazioni
  • Scopus 1
  • ???jsp.display-item.citation.isi??? 0
Social impact