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.
Sensitivity analysis of solutions for a system of generalized parametric nonlinear quasivariational inequalities.
Sensitivity analysis of solutions to a class of quasi-variational inequalities
We provide a sensitivity result for the solutions to the following finite-dimensional quasi-variational inequality when both the operator and the convex are perturbed. In particular, we prove the Hölder continuity of the solution sets of the problems perturbed around the original problem. All the results may be extended to infinite-dimensional (QVI).
Sensitivity of optimal solutions to control problems for systems described by hemivariational inequalities
Sensitivity of optimal solutions to control problems for systems described by hemivariational inequalities
Shape and topological sensitivity analysis in domains with cracks
The framework for shape and topology sensitivity analysis in geometrical domains with cracks is established for elastic bodies in two spatial dimensions. The equilibrium problem for the elastic body with cracks is considered. Inequality type boundary conditions are prescribed at the crack faces providing a non-penetration between the crack faces. Modelling of such problems in two spatial dimensions is presented with all necessary details for further applications in shape optimization in structural...
Shape optimization in contact problems. Approximation and numerical realization
Shape optimization in contact problems based on penalization of the state inequality
The paper deals with the approximation of optimal shape of elastic bodies, unilaterally supported by a rigid, frictionless foundation. Original state inequality, describing the behaviour of such a body is replaced by a family of penalized state problems. The relation between optimal shapes for the original state inequality and those for penalized state equations is established.
Shape optimization in two-dimensional elasticity by the dual finite element method
Shape optimization of an elasto-plastic body for the model with strain- hardening
The state problem of elasto-plasticity (for the model with strain-hardening) is formulated in terms of stresses and hardening parameters by means of a time-dependent variational inequality. The optimal design problem is to find the shape of a part of the boundary such that a given cost functional is minimized. For the approximate solutions piecewise linear approximations of the unknown boundary, piecewise constant triangular elements for the stress and the hardening parameter, and backward differences...