1. General Versions of the Ekeland Variational Principle: Ekeland Points and Stop and Go Dynamics
- Author
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Le Phuoc Hai, Phan Quoc Khanh, Antoine Soubeyran, University of Science – Vietnam National University Ho Chi Minh City, Ho Chi Minh City, Vietnam, Ton Duc Thang University [Hô-Chi-Minh-City], Aix-Marseille Sciences Economiques (AMSE), École des hautes études en sciences sociales (EHESS)-Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS), National Foundation for Science and Technology Development (NAFOSTED) of Vietnam under Grant 101.01-2021.13, ANR-17-EURE-0020,AMSE (EUR),Aix-Marseille School of Economics(2017), and ANR-11-IDEX-0001,Amidex,INITIATIVE D'EXCELLENCE AIX MARSEILLE UNIVERSITE(2011)
- Subjects
Ekeland points ,Partial quasi-metric space ,Variational trap ,Control and Optimization ,Stop and go dynamics ,Applied Mathematics ,Two perturbation bifunctions ,90C30 ,49J52 ,49J53 ,90C26 ,91E45 ,Ekeland variational principle ,Management Science and Operations Research ,[SHS.ECO]Humanities and Social Sciences/Economics and Finance ,Better perturbation ,Worthwhile move - Abstract
International audience; We establish general versions of the Ekeland variational principle (EVP), where we include two perturbation bifunctions to discuss and obtain better perturbations for obtaining three improved versions of the principle. Here, unlike the usual studies and applications of the EVP, which aim at exact minimizers via a limiting process, our versions provide good-enough approximate minimizers aiming at applications in particular situations. For the presentation of applications chosen in this paper, the underlying space is a partial quasi-metric one. To prove the aforementioned versions, we need a new proof technique. The novelties of the results are in both theoretical and application aspects. In particular, for applications, using our versions of the EVP together with new concepts of Ekeland points and stop and go dynamics, we study in detail human dynamics in terms of a psychological traveler problem, a typical model in behavioral sciences.
- Published
- 2022