955 research outputs found
Fuzzy games with a countable space of actions and applications to systems of generalized quasi-variational inequalities
In this paper, we introduce an abstract fuzzy economy (generalized fuzzy
game) model with a countable space of actions and we study the existence of the
fuzzy equilibrium. As applications, two types of results are obtained. The
first ones concern the existence of the solutions for systems of generalized
quasi-variational inequalities with random fuzzy mappings which we define. The
last ones are new random fixed point theorems for correspondences with values
in complete countable metric spaces.Comment: 18 page
A class of Hamilton-Jacobi equations on Banach-Finsler manifolds
The concept of subdifferentiability is studied in the context of
Finsler manifolds (modeled on a Banach space with a Lipschitz bump
function). A class of Hamilton-Jacobi equations defined on Finsler
manifolds is studied and several results related to the existence and
uniqueness of viscosity solutions are obtained.Comment: 24 page
Stability analysis of partial differential variational inequalities in Banach spaces
In this paper, we study a class of partial differential variational inequalities. A general stability result for the partial differential variational inequality is provided in the case the perturbed parameters are involved in both the nonlinear mapping and the set of constraints. The main tools are theory of semigroups, theory of monotone operators, and variational inequality techniques
Optimal Control of Delay-Differential Inclusions with Multivalued Initial Conditions in Infinite Dimensions
This paper is devoted to the study of a general class of optimal control problems described by delay-differential inclusions with infinite-dimensional state spaces, endpoints constraints, and multivalued initial conditions. To the best of our knowledge, problems of this type have not been considered in the literature, except some particular cases when either the state space is finite-dimensional or there is no delay in the dynamics. We develop the method of discrete approximations to derive necessary optimality conditions in the extended Euler-Lagrange form by using advanced tools of variational analysis and generalized differentiation in infinite dimensions. This method consists of the three major parts: (a) constructing a well-posed sequence of discrete-time problems that approximate in an appropriate sense the original continuous-time problem of dynamic optimization; (b) deriving necessary optimality conditions for the approximating discrete-time problems by reducing them to infinite-dimensional problems of mathematical programming and employing then generalized differential calculus; (c) passing finally to the limit in the obtained results for discrete approximations to establish necessary conditions for the given optimal solutions to the original problem. This method is fully realized in the delay-differential systems under consideration
Some aspects of variational inequalities
AbstractIn this paper we provide an account of some of the fundamental aspects of variational inequalities with major emphasis on the theory of existence, uniqueness, computational properties, various generalizations, sensitivity analysis and their applications. We also propose some open problems with sufficient information and references, so that someone may attempt solution(s) in his/her area of special interest. We also include some new results, which we have recently obtained
Local strong maximal monotonicity and full stability for parametric variational systems
The paper introduces and characterizes new notions of Lipschitzian and
H\"olderian full stability of solutions to general parametric variational
systems described via partial subdifferential and normal cone mappings acting
in Hilbert spaces. These notions, postulated certain quantitative properties of
single-valued localizations of solution maps, are closely related to local
strong maximal monotonicity of associated set-valued mappings. Based on
advanced tools of variational analysis and generalized differentiation, we
derive verifiable characterizations of the local strong maximal monotonicity
and full stability notions under consideration via some positive-definiteness
conditions involving second-order constructions of variational analysis. The
general results obtained are specified for important classes of variational
inequalities and variational conditions in both finite and infinite dimensions
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