Regularization of a unilateral obstacle problem on the boundary.
Relatively B-pseudomonotone variational inequalities over product of sets.
Reliable solution of parabolic obstacle problems with respect to uncertain data
A class of parabolic initial-boundary value problems is considered, where admissible coefficients are given in certain intervals. We are looking for maximal values of the solution with respect to the set of admissible coefficients. We give the abstract general scheme, proposing how to solve such problems with uncertain data. We formulate a general maximization problem and prove its solvability, provided all fundamental assumptions are fulfilled. We apply the theory to certain Fourier obstacle type...
Remark to dynamic contact problems for bodies with a singular memory
The existence of a solution to the dynamic contact of a body having a singular memory with a rigid undeformable support is proved under some weaker assumption than that in [3].
Remarks on some fourth order variational inequalities
Remarks on the Regularity of Weak Solutions to Some Variational Inequalities.
Resolvent iterative methods for solving system of extended general variational inclusions.
Revisiting the construction of gap functions for variational inequalities and equilibrium problems via conjugate duality
Based on conjugate duality we construct several gap functions for general variational inequalities and equilibrium problems, in the formulation of which a so-called perturbation function is used. These functions are written with the help of the Fenchel-Moreau conjugate of the functions involved. In case we are working in the convex setting and a regularity condition is fulfilled, these functions become gap functions. The techniques used are the ones considered in [Altangerel L., Boţ R.I., Wanka...
Robinson's implicit function theorem
s-coincidence and s-common fixed point theorems for two pairs of set-valued noncompatible mappings in two pairs of set-valued noncompatible mappings in metric space.
Second-Order Boundary regularity for quasilinear variational inequalities.
Self-adaptive implicit methods for monotone variant variational inequalities.
Semi-group methods in stochastic control
Semi–smooth Newton methods for variational inequalities of the first kind
Semi–smooth Newton methods are analyzed for a class of variational inequalities in infinite dimensions. It is shown that they are equivalent to certain active set strategies. Global and local super-linear convergence are proved. To overcome the phenomenon of finite speed of propagation of discretized problems a penalty version is used as the basis for a continuation procedure to speed up convergence. The choice of the penalty parameter can be made on the basis of an estimate for the penalized...
Semi–Smooth Newton Methods for Variational Inequalities of the First Kind
Semi–smooth Newton methods are analyzed for a class of variational inequalities in infinite dimensions. It is shown that they are equivalent to certain active set strategies. Global and local super-linear convergence are proved. To overcome the phenomenon of finite speed of propagation of discretized problems a penalty version is used as the basis for a continuation procedure to speed up convergence. The choice of the penalty parameter can be made on the basis of an L∞ estimate for the penalized...
Semi-strong convergence of sequences satisfying a variational inequality
Sensitivity analysis for variational inclusions by Wiener-Hopf equation techniques.
Sensitivity analysis of a nonlinear obstacle plate problem
We analyse the sensitivity of the solution of a nonlinear obstacle plate problem, with respect to small perturbations of the middle plane of the plate. This analysis, which generalizes the results of [9, 10] for the linear case, is done by application of an abstract variational result [6], where the sensitivity of parameterized variational inequalities in Banach spaces, without uniqueness of solution, is quantified in terms of a generalized derivative, that is the proto-derivative. We prove that...
Sensitivity Analysis of a Nonlinear Obstacle Plate Problem
We analyse the sensitivity of the solution of a nonlinear obstacle plate problem, with respect to small perturbations of the middle plane of the plate. This analysis, which generalizes the results of [9,10] for the linear case, is done by application of an abstract variational result [6], where the sensitivity of parameterized variational inequalities in Banach spaces, without uniqueness of solution, is quantified in terms of a generalized derivative, that is the proto-derivative. We prove that...
Sensitivity analysis of extended general variational inequalities.