Variational principles with generalized distances and the modelization of organizational change

Abstract

This paper has a two-fold focus. The mathematical aspect of the paper shows that new and existing quasimetric and weak τ -distance versions of Ekeland's variational principle are equivalent in the sense that one implies the other, and so are their corresponding fixed-point results. The practical aspect of the paper, using a recent variational rationality approach of human behavior, offers a model of organizational change, where generalized distances model inertia in terms of resistance to change. The formation and breaking of routines relative to hiring and firing workers will be used to illustrate the obtained results.

On extended versions of Dancs-Hegedüs-Medvegyev’s fixed-point theorem

“…These "metrics" have some interest in topology, but they are also used in applied mathematics in the calculus of variation. Recently, Bao et al studied in [8,15,16] some mathematical models arising in some areas of behavioral sciences (called sometimes "theories of stability/stay and change"). It seems that everyone agrees that the cost to change in these models does not satisfy the symmetry property.…”

“…the topology τ r in the aforementioned references, and left sequential convergence in [6][7][8]15] and many references therein. The forward Cauchy sequence is known as left-sequential Cauchy (also as lelf Cauchy or Cauchy) sequence in Bao et al [6][7][8], left-K-Cauchy in Reilly et al [26]. The backward Cauchy notion is known as p-Cauchy in [25, Definition 2.10], right-K-Cauchy in Reilly et al [26].…”

“…It has provided simple and elegant proofs of known results such as the Caristi fixed point theorem in complete metric spaces [3] (in fact the two results are equivalent). It is well established that Dancs-Hegedüs-Medvegyev's fixed point theorem [4,Theorem 3.1] has served as a significant tool in proving Ekeland's variational principle [5] and its extensions to vector and set optimization; the reader is referred for instance to [6][7][8][9][10][11][12][13]. It is important to emphasize that the Dancs-Hegedüs-Medvegyev fixed point theorem is equivalent to Ekeland's variational principle [5] in the sense that one implies the other.…”

General descent method using w-distance. Application to emergence of habits following worthwhile moves

“…Next, we give some classical examples of w-distance, which can be found, for instance, in [31] and Suzuki and Takahashi [32]. To this end, let X be a metric space with metric d. The application of w-distance in organizational change can be found in Bao, Khanh and Soubeyran [4].…”

Variational principles in set optimization with domination structures and application to changing jobs

“…; see the references above. Recently, set-valued and set optimization with variable ordering structure have been extensively studied in [5,6,7,8,9,10,18,19,33,34] and references therein.…”