33 research outputs found
A Convergence Criterion for Elliptic Variational Inequalities
We consider an elliptic variational inequality with unilateral constraints in
a Hilbert space which, under appropriate assumptions on the data, has a
unique solution . We formulate a convergence criterion to the solution ,
i.e., we provide necessary and sufficient conditions on a sequence
which guarantee the convergence in the space .
Then, we illustrate the use of this criterion to recover well-known convergence
results and well-posedness results in the sense of Tykhonov and Levitin-Polyak.
We also provide two applications of our results, in the study of a heat
transfer problem and an elastic frictionless contact problem, respectively.Comment: 26 pages. arXiv admin note: text overlap with arXiv:2005.1178
Generalized Well-Posedness for Symmetric Vector Quasi-Equilibrium Problems
We introduce and study well-posedness in connection with the symmetric vector quasi-equilibrium problem, which unifies its Hadamard and Levitin-Polyak well-posedness. Using the nonlinear scalarization function, we give some sufficient conditions to guarantee the existence of well-posedness for the symmetric vector quasi-equilibrium problem
Well-posedness, a short survey
In this paper we analyze the property of Tykhonov wellposedness
in relation to other well-posedness properties
which are ordinal and, as stated in the title, we give a
survey on some important results on well-posedness in
scalar optimization and in scalar inequalities
α
The concepts of α-well-posedness, α-well-posedness in the
generalized sense, L-α-well-posedness and L-α-well-posedness in the generalized sense for
mixed quasi variational-like inequality problems are investigated. We present some metric
characterizations for these well-posednesses
Well-Posedness by Perturbations for Variational-Hemivariational Inequalities
We generalize the concept of well-posedness by perturbations for optimization problem to a class of variational-hemivariational inequalities. We establish some metric characterizations of the well-posedness by perturbations for the variational-hemivariational inequality and prove their equivalence between the well-posedness by perturbations for the variational-hemivariational inequality and the well-posedness by perturbations for the corresponding inclusion problem