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Variational principles, completeness and the existence of traps in behavioral sciences

Bao Q. Truong (btruong***at***nmu.edu)
Antoine Soubeyran (antoine.soubeyran***at***gmail.com)
Stephan Cobza\c{s} (scobzas***at***math.ubbcluj.ro)

Abstract: In this paper, driven by Behavioral applications to human dynamics, we consider the characterization of completeness in pseudo-quasimetric spaces in term of a generalization of Ekeland's variational principle in such spaces, and provide examples illustrating significant improvements to some previously obtained results, even in complete metric spaces. At the behavioral level, we show that the completeness of a space is equivalent to the existence of traps, rather easy to reach (in a worthwhile way), but difficult (not worthwhile to) to leave. We first establish new forward and backward versions of Ekeland's variational principle for the class of strict-decreasingly forward (resp. backward)-lower-semicontinuous functions in pseudo-quasimetric spaces. We do not require that the space under consideration either be complete or to enjoy the limit uniqueness property since, in a pseudo-quasimetric space, the collections of forward-limits and backward ones of a sequence, in general, are not singletons.

Keywords: Pseudo-quasimetric; Forward-completeness; Backward-completeness; Variational principle; Group dynamics; Existence of trap.

Category 1: Nonlinear Optimization (Other )

Category 2: Applications -- Science and Engineering (Other )


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Entry Submitted: 09/02/2015
Entry Accepted: 09/02/2015
Entry Last Modified: 03/30/2016

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