Sensitivity analysis for relaxed cocoercive nonlinear quasivariational inclusions.
Sensitivity analysis for variational inclusions by Wiener-Hopf equation techniques.
Sensitivity analysis of extended general variational inequalities.
Solving variational inclusions by a multipoint iteration method under center-Hölder continuity conditions
We prove the existence of a sequence satisfying , where f is a function whose second order Fréchet derivative ∇²f satifies a center-Hölder condition and F is a set-valued map from a Banach space X to the subsets of a Banach space Y. We show that the convergence of this method is superquadratic.
Some new deterministic and random variational inequalities and their applications.
Some new existence, sensitivity and stability results for the nonlinear complementarity problem
In this work we study the nonlinear complementarity problem on the nonnegative orthant. This is done by approximating its equivalent variational-inequality-formulation by a sequence of variational inequalities with nested compact domains. This approach yields simultaneously existence, sensitivity, and stability results. By introducing new classes of functions and a suitable metric for performing the approximation, we provide bounds for the asymptotic set of the solution set and coercive existence...
Stability of a variational inequality with respect to domain perturbations.
Stability of Noor iterations with errors for generalized nonlinear complementarity problems.
Strong convergence of a modified iterative algorithm for mixed-equilibrium problems in Hilbert spaces.
Strong convergence of an iterative method for variational inequality problems and fixed point problems
In this paper, we introduce a general iterative scheme to investigate the problem of finding a common element of the fixed point set of a strict pseudocontraction and the solution set of a variational inequality problem for a relaxed cocoercive mapping by viscosity approximate methods. Strong convergence theorems are established in a real Hilbert space.
Strong convergence of viscosity iteration methods for nonexpansive mappings.
Structure of stable solutions of a one-dimensional variational problem
We prove the periodicity of all H2-local minimizers with low energy for a one-dimensional higher order variational problem. The results extend and complement an earlier work of Stefan Müller which concerns the structure of global minimizer. The energy functional studied in this work is motivated by the investigation of coherent solid phase transformations and the competition between the effects from regularization and formation of small scale structures. With a special choice of a bilinear double...
Study of a viscoelastic frictional contact problem with adhesion
We consider a quasistatic frictional contact problem between a viscoelastic body with long memory and a deformable foundation. The contact is modelled with normal compliance in such a way that the penetration is limited and restricted to unilateral constraint. The adhesion between contact surfaces is taken into account and the evolution of the bonding field is described by a first order differential equation. We derive a variational formulation and prove the existence and uniqueness result of the...
Sufficient optimality conditions and semi-smooth newton methods for optimal control of stationary variational inequalities
In this paper sufficient second order optimality conditions for optimal control problems subject to stationary variational inequalities of obstacle type are derived. Since optimality conditions for such problems always involve measures as Lagrange multipliers, which impede the use of efficient Newton type methods, a family of regularized problems is introduced. Second order sufficient optimality conditions are derived for the regularized problems...
Sufficient optimality conditions and semi-smooth newton methods for optimal control of stationary variational inequalities
In this paper sufficient second order optimality conditions for optimal control problems subject to stationary variational inequalities of obstacle type are derived. Since optimality conditions for such problems always involve measures as Lagrange multipliers, which impede the use of efficient Newton type methods, a family of regularized problems is introduced. Second order sufficient optimality conditions are derived for the regularized problems...
System of general variational inequalities involving different nonlinear operators related to fixed point problems and its applications.
System of generalized implicit vector quasivariational inequalities.