General Versions of the Ekeland Variational Principle: Ekeland Points and Stop and Go Dynamics

Le Phuoc Hai, Phan Quoc Khanh and Antoine Soubeyran
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Le Phuoc Hai: HCMUS - Ho Chi Minh City University of Science [Vietnam National University, HCM]
Phan Quoc Khanh: Ton Duc Thang University [Hô-Chi-Minh-City]

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Abstract: 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.

Keywords: Stop and go dynamics; Variational trap; Worthwhile move; Partial quasi-metric space; Ekeland points; Better perturbation; Two perturbation bifunctions; Ekeland variational principle (search for similar items in EconPapers)
Date: 2022-10-01
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Published in Journal of Optimization Theory and Applications, 2022, 195 (1), pp.347-373. ⟨10.1007/s10957-022-02087-y⟩

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Journal Article: General Versions of the Ekeland Variational Principle: Ekeland Points and Stop and Go Dynamics (2022)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-03784715

DOI: 10.1007/s10957-022-02087-y

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