Displaying similar documents to “Relations between multidimensional interval-valued variational problems and variational inequalities”

New extension of the variational McShane integral of vector-valued functions

Sokol Bush Kaliaj (2019)

Mathematica Bohemica

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We define the Hake-variational McShane integral of Banach space valued functions defined on an open and bounded subset G of m -dimensional Euclidean space ℝ m . It is a “natural” extension of the variational McShane integral (the strong McShane integral) from m -dimensional closed non-degenerate intervals to open and bounded subsets of ℝ m . We will show a theorem that characterizes the Hake-variational McShane integral in terms of the variational McShane integral. This theorem reduces the study...

Local analysis of a cubically convergent method for variational inclusions

Steeve Burnet, Alain Pietrus (2011)

Applicationes Mathematicae

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This paper deals with variational inclusions of the form 0 ∈ φ(x) + F(x) where φ is a single-valued function admitting a second order Fréchet derivative and F is a set-valued map from ℝ q to the closed subsets of ℝ q . When a solution z̅ of the previous inclusion satisfies some semistability properties, we obtain local superquadratic or cubic convergent sequences.

Duality for a fractional variational formulation using η -approximated method

Sony Khatri, Ashish Kumar Prasad (2023)

Kybernetika

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The present article explores the way η -approximated method is applied to substantiate duality results for the fractional variational problems under invexity. η -approximated dual pair is engineered and a careful study of the original dual pair has been done to establish the duality results for original problems. Moreover, an appropriate example is constructed based on which we can validate the established dual statements. The paper includes several recent results as special cases. ...

A penalty approach for a box constrained variational inequality problem

Zahira Kebaili, Djamel Benterki (2018)

Applications of Mathematics

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We propose a penalty approach for a box constrained variational inequality problem ( BVIP ) . This problem is replaced by a sequence of nonlinear equations containing a penalty term. We show that if the penalty parameter tends to infinity, the solution of this sequence converges to that of BVIP when the function F involved is continuous and strongly monotone and the box C contains the origin. We develop the algorithmic aspect with theoretical arguments properly established. The numerical results...

On discontinuous quasi-variational inequalities

Liang-Ju Chu, Ching-Yang Lin (2007)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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In this paper, we derive a general theorem concerning the quasi-variational inequality problem: find x̅ ∈ C and y̅ ∈ T(x̅) such that x̅ ∈ S(x̅) and ⟨y̅,z-x̅⟩ ≥ 0, ∀ z ∈ S(x̅), where C,D are two closed convex subsets of a normed linear space X with dual X*, and T : X → 2 X * and S : C → 2 D are multifunctions. In fact, we extend the above to an existence result proposed by Ricceri [12] for the case where the multifunction T is required only to satisfy some general assumption without any continuity. Under a...

Anti-periodic solutions to a parabolic hemivariational inequality

Jong Yeoul Park, Hyun Min Kim, Sun Hye Park (2004)

Kybernetika

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In this paper we deal with the anti-periodic boundary value problems with nonlinearity of the form b ( u ) , where b ∈ L loc ∞ ( R ) . Extending b to be multivalued we obtain the existence of solutions to hemivariational inequality and variational-hemivariational inequality.

The Dirichlet problem with sublinear nonlinearities

Aleksandra Orpel (2002)

Annales Polonici Mathematici

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We investigate the existence of solutions of the Dirichlet problem for the differential inclusion 0 ∈ Δ x ( y ) + ∂ x G ( y , x ( y ) ) for a.e. y ∈ Ω, which is a generalized Euler-Lagrange equation for the functional J ( x ) = ∫ Ω 1 / 2 | ∇ x ( y ) | ² - G ( y , x ( y ) ) d y . We develop a duality theory and formulate the variational principle for this problem. As a consequence of duality, we derive the variational principle for minimizing sequences of J. We consider the case when G is subquadratic at infinity.

Analysis of approximate solutions of coupled dynamical thermoelasticity and related problems

Jozef Kačur, Alexander Ženíšek (1986)

Aplikace matematiky

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The authors study problems of existence and uniqueness of solutions of various variational formulations of the coupled problem of dynamical thermoelasticity and of the convergence of approximate solutions of these problems. First, the semidiscrete approximate solutions is defined, which is obtained by time discretization of the original variational problem by Euler’s backward formula. Under certain smoothness assumptions on the date authors prove existence and uniqueness of the solution...

Some remarks on descriptive characterizations of the strong McShane integral

Sokol Bush Kaliaj (2019)

Mathematica Bohemica

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We present the full descriptive characterizations of the strong McShane integral (or the variational McShane integral) of a Banach space valued function f : W → X defined on a non-degenerate closed subinterval W of ℝ m in terms of strong absolute continuity or, equivalently, in terms of McShane variational measure V ℳ F generated by the primitive F : ℐ W → X of f , where ℐ W is the family of all closed non-degenerate subintervals of W .