Vector Variational Inequalities and Vector Optimization

Variational Analysis and Variational Rationality in Behavioral Sciences: Stationary Traps

“…• Developments and applications of the extremal principle and related tools of variational analysis to problems with variable cone preferences, which naturally arise in behavioral sciences via the variational rationality approach; see [4,5] and also compare it with the books [1,8,10] treated general multiobjective optimization problems of this type.…”

“…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.Recent years have witnessed broad applications of advanced tools of variational analysis, generalized differentiation, and multiobjective (vector and set-valued) optimization to real-life models, particularly those related to economics and finance; see, e.g., [1,3,8,10,11,12] and the references therein. Lately [4,5], certain variational principles and techniques have been developed and applied to models of behavioral sciences that mainly concern human behavior.…”

“…Recent years have witnessed broad applications of advanced tools of variational analysis, generalized differentiation, and multiobjective (vector and set-valued) optimization to real-life models, particularly those related to economics and finance; see, e.g., [1,3,8,10,11,12] and the references therein. Lately [4,5], certain variational principles and techniques have been developed and applied to models of behavioral sciences that mainly concern human behavior.…”

“…Ekeland variational principle in the case of set-valued mappings defined on quasimetric spaces and taken values in vector spaces with variable ordering structures; see also [1,8,10] for multiobjective optimization problems of this type.…”

Ekeland variational principles for vector equilibrium problems with solid ordering cones

“…The paper deals with versions of this result for vector bifunctions. Nowadays, these variational principles are a growing research line (see [1,4,6,10,14,15,19,20,21]) since they can be formulated as vector equilibrium problems, which encompass several really important problems, like vector optimization problems, vector variational inequalities and vector complementary problems (see [2,3,7,11,17] and the references therein). This work is motivated by the recent Ekeland variational principles in [15], where they are derived by considering the so-called Gerstewitz scalarization functional and a kind of proper approximate solutions of vector equilibrium problems.…”