Abstract
In this paper, we introduce a new proximal algorithm for equilibrium problems on a genuine Hadamard manifold, using a new regularization term. We first extend recent existence results by considering pseudomonotone bifunctions and a weaker sufficient condition than the coercivity assumption. Then, we consider the convergence of this proximal-like algorithm which can be applied to genuinely Hadamard manifolds and not only to specific ones, as in the recent literature. A striking point is that our new regularization term have a clear interpretation in a recent “variational rationality” approach of human behavior. It represents the resistance to change aspects of such human dynamics driven by motivation to change aspects. This allows us to give an application to the theories of desires, showing how an agent must escape to a succession of temporary traps to be able to reach, at the end, his desires.
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Acknowledgements
Funding was provided by Conselho Nacional de Desenvolvimento Científico e Tecnológico (Grant Nos. 423737/2016-3, 310864/2017-8, 308330/2018-8) and Fundação de Amparo à Pesquisa do Estado de Goiás (PRONEN Grant No. 201710267000532). The authors wish to express their gratitude to the anonymous referees for their comments and suggestions that contributed to a significant improvement in the paper.
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Bento, G.C., Neto, J.X.C., Soares, P.A. et al. A new regularization of equilibrium problems on Hadamard manifolds: applications to theories of desires. Ann Oper Res 316, 1301–1318 (2022). https://doi.org/10.1007/s10479-021-04052-w
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DOI: https://doi.org/10.1007/s10479-021-04052-w