By using a pre-order principle in [Qiu JH. A pre-order principle and set-valued Ekeland variational principle. J Math Anal Appl. 2014;419:904–937], we establish a general equilibrium version of set-valued Ekeland variational principle (denoted by EVP), where the objective function is a set-valued bimap defined on the product of left-complete quasi-metric spaces and taking values in a quasi-ordered linear space, and the perturbation consists of a cone-convex subset of the ordering cone multiplied by the quasi-metric. Moreover, we obtain an equilibrium EVP, where the perturbation contains a σ-convex subset and the quasi-metric. From the above two general EVPs, we deduce several interesting corollaries, which extend and improve the related known results. Several examples show that the obtained set-valued EVPs are new. Finally, applying the above EVPs to organizational behavior sciences, we obtain some interesting results on organizational change and development with leadership. In particular, we show that the existence of robust organizational traps.

In this paper, we extend the general descent method proposed by Attouch, Bolte and Svaiter [Math. Program. 137 (2013), 91-129] to deal with possible asymmetric like-distances. Using a w-distance as regularization term our results guarantee the convergence of bounded sequences, under the assumption that the objective function satisfies the Kurdyka-Łojasiewicz inequality. In particular, it improves some existing works on proximal point methods with quasi-distance as regularization term because we prove convergence of bounded sequences without any additional assumption on the w-distance unlike it have been done with quasi-distances. The last section gives an application relative to the emergence of habits after a succession of worthwhile moves which balance motivation and resistance to move.

We consider the constrained multi-objective optimization problem of finding Pareto critical points of difference of convex functions. The new approach proposed by Bento et al. (SIAM J Optim 28:1104–1120, 2018) to study the convergence of the proximal point method is applied. Our method minimizes at each iteration a convex approximation instead of the (non-convex) objective function constrained to a possibly non-convex set which assures the vector improving process. The motivation comes from the famous Group Dynamic problem in Behavioral Sciences where, at each step, a group of (possible badly informed) agents tries to increase his joint payoff, in order to be able to increase the payoff of each of them. In this way, at each step, this ascent process guarantees the stability of the group. Some encouraging preliminary numerical results are reported.

This paper concerns applications of variational analysis to some local aspects of behavioral science modeling by developing an effective variational rationality approach to these and related issues. Our main attention is paid to local stationary traps, which reflect such local equilibrium and the like positions in behavioral science models that are not worthwhile to quit. We establish constructive linear optimistic evaluations of local stationary traps by using generalized differential tools of variational analysis that involve subgradients and normals for nonsmooth and nonconvex objects as well as variational and extremal principles.