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A note on Minty type vector variational inequalities

Giovanni P. Crespi, Ivan Ginchev, Matteo Rocca (2005)

RAIRO - Operations Research - Recherche Opérationnelle

The existence of solutions to a scalar Minty variational inequality of differential type is usually related to monotonicity property of the primitive function. On the other hand, solutions of the variational inequality are global minimizers for the primitive function. The present paper generalizes these results to vector variational inequalities putting the Increasing Along Rays (IAR) property into the center of the discussion. To achieve that infinite elements in the image space Y are introduced....

A note on Minty type vector variational inequalities

Giovanni P. Crespi, Ivan Ginchev, Matteo Rocca (2006)

RAIRO - Operations Research

The existence of solutions to a scalar Minty variational inequality of differential type is usually related to monotonicity property of the primitive function. On the other hand, solutions of the variational inequality are global minimizers for the primitive function. The present paper generalizes these results to vector variational inequalities putting the Increasing Along Rays (IAR) property into the center of the discussion. To achieve that infinite elements in the image space Y are introduced. Under...

A note on solutions of semilinear equations at resonance in a cone

Bogdan Przeradzki (1993)

Annales Polonici Mathematici

A connection between the Landesman-Lazer condition and the solvability of the equation Lx = N(x) in a cone with a noninvertible linear operator L is studied. The result is based on the abstract framework from [5], applied to the existence of periodic solutions of ordinary differential equations, and compared with theorems by Santanilla (see [7]).

A parameter choice for Tikhonov regularization for solving nonlinear inverse problems leading to optimal convergence rates

Otmar Scherzer (1993)

Applications of Mathematics

We give a derivation of an a-posteriori strategy for choosing the regularization parameter in Tikhonov regularization for solving nonlinear ill-posed problems, which leads to optimal convergence rates. This strategy requires a special stability estimate for the regularized solutions. A new proof fot this stability estimate is given.

A penalty approach for a box constrained variational inequality problem

Zahira Kebaili, Djamel Benterki (2018)

Applications of Mathematics

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 tested on...

A principle of linearization in theory of stability of solutions of variational inequalities

Jiří Neustupa (1995)

Mathematica Bohemica

It is shown that the uniform exponential stability and the uniform stability at permanently acting disturbances of a sufficiently smooth but not necessarily steady-state solution of a general variational inequality is a consequence of the uniform exponential stability of a zero solution of another (so called linearized) variational inequality.

A quasistatic bilateral contact problem with adhesion and friction for viscoelastic materials

Arezki Touzaline (2010)

Commentationes Mathematicae Universitatis Carolinae

We consider a mathematical model which describes a contact problem between a deformable body and a foundation. The contact is bilateral and is modelled with Tresca's friction law in which adhesion is taken into account. The evolution of the bonding field is described by a first order differential equation and the material's behavior is modelled with a nonlinear viscoelastic constitutive law. We derive a variational formulation of the mechanical problem and prove the existence and uniqueness result...

Currently displaying 101 – 120 of 283