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: University of Science
Phan Quoc Khanh: Ton Duc Thang University

Journal of Optimization Theory and Applications, 2022, vol. 195, issue 1, No 16, 347-373

Abstract: 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: Ekeland variational principle; Two perturbation bifunctions; Better perturbation; Ekeland points; Partial quasi-metric space; Worthwhile move; Variational trap; Stop and go dynamics; 90C30; 49J52; 49J53; 90C26; 91E45 (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-022-02087-y

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