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

Stefano Lucidi (), Mauro Passacantando () and Francesco Rinaldi ()
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Stefano Lucidi: Sapienza University of Rome
Mauro Passacantando: University of Pisa
Francesco Rinaldi: University of Padova

Journal of Global Optimization, 2022, vol. 83, issue 4, No 3, 699-725

Abstract: 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.

Keywords: Equilibrium problem; Gap function; Global optimization; DIRECT algorithm; 90C26; 90C33; 90C56 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10898-021-01121-z

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