The classification of the possible equilibrium shapes that a selfgravitating fluid can take in a Riemannian manifold is a classical problem in mathematical physics. In this paper it is proved that the equilibrium shapes are isoparametric submanifolds. Some geometric properties of the equilibrium shapes are also obtained, specifically the relationship with the isoperimetric problem and the group...

It is well known that variational inequalities are systematically used in the theory of many practical problems related to ”equilibrium”. The equilibrium is an important state considered in Physics, Engineering, Sciences and Economics and even in Biology, [5], [37], [38], [24], [56]. When a variational inequality is defined on a closed convex set, which is in particular a closed convex cone, in...

We introduce and study a new class of auxiliary problems for solving the equilibrium problem in Banach spaces. Not only the existence of approximate solutions of the equilibrium problem is proven, but also the strong convergence of approximate solutions to an exact solution of the equilibrium problem is shown. Furthermore, we give some iterative schemes for solving some generalizedmixed variati...

In this paper, we consider strong form of a vector equilibrium problem and establish some existence results for solutions of such problem in the setting of topological vector spaces. We provide several coercivity conditions under which strong vector equilibrium problem has a solution. Our results generalize and extend the results of Bianchi and Pini [Coercivity conditions for equilibrium proble...

This report includes a modern account of welfare economics and competitive equilibrium theory. In particular, competitive, or Walrasian, equilibrium is defined. Moreover, existence, optimality, and uniqueness are demonstrated. However, no reliable mechanism for computing equilibrium prices is suggested. At this stage, the problem shifts from the realm of economics to an algorithmic problem in c...

We consider an equilibrium problem defined on a convex set, whose cost bifunction may not be monotone. We show that this problem can be solved by the inexact partial proximal method with quasi distance. As an application, at the psychological level of behavioral dynamics, this paper shows two points: i) how a dual equilibrium problem offers a model of behavioral trap, “easy enough to reach, dif...

We consider the problem of computing equilibrium prices for exchange economies. We tackle this problem under the assumption that the traders have either CES (constant elasticity of substitution) utility functions or a subfamily of ASC (additively separable concave) utilities. For the subfamily of ASC functions, and for a range of CES functions which include some CES functions that do not satisf...

The article considers a particular class of optimization problems involving set-valued stochastic equilibrium constraints. A solution procedure is developed by relying on an approximation scheme for the equilibrium constraints, based on regularization, that replaces them by equilibrium constraints involving only single-valued Lipschitz continuous functions. In addition, sampling has the further...

Given a network with a continuum of users at some origins, suppose that the users wish to reach specific destinations, but that they are not indifferent to the time needed to reach their destination. They may have several possibilities (of routes or deparure time), but their choices modify the travel times on the network. Hence, each user faces the following problem: given a pattern of travel t...