A Study of Regularization Techniques of Nondifferentiable Optimization in View of Application to Hemivariational Inequalities

Ovcharova, Nina; Gwinner, Joachim

doi:10.1007/s10957-014-0521-y

Cited by 29 publications

(19 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Here also interesting parameter identification problems arise. When the nonmonotone boundary conditions are of max or min or min-max type, advanced regularization techniques, see [27,19] for the forward problem, are applicable.…”

Section: Concluding Remarks -An Outlookmentioning

confidence: 99%

An optimization approach to parameter identification in variational inequalities of second kind

Gwinner

2017

Optim Lett

Self Cite

View full text Add to dashboard Cite

This paper continues the work of [16] and is concerned with the inverse problem of parameter identification in variational inequalities of the second kind that does not only treat the parameter linked to a bilinear form, but importantly also the parameter linked to a nonlinear non-smooth function. Here we specify the abstract framework of [16] and cover frictional contact problems as well as other non-smooth problems from continuum mechanics. The optimization approach of [16] to the inverse problem using the output-least squares formulation involves the variational inequality of the second kind as constraint. Here we use regularization technics of nondifferentiable optimization from [10], regularize the nonsmooth part in the variational inequality and arrive at an optimization problem for which the constraint variational inequality is replaced by the regularized variational equation. For this case, the smoothness of the parameter-to-solution map is studied and convergence analysis and optimality conditions are given.

show abstract

Section: Concluding Remarks -An Outlookmentioning

confidence: 99%

An optimization approach to parameter identification in variational inequalities of second kind

Gwinner

2017

Optim Lett

Self Cite

View full text Add to dashboard Cite

show abstract

“…Theorem 6.1 [37] (General approximation result) Under the hypotheses (H1)-(H6), there exist a solution ut to the approximate problem V I(ψt , ft , Kt ) and the family {ut } is bounded in X. Moreover, there exists a subnet of {ut } that converges weakly in X to a solution of the problem V I(ψ, f , K).…”

Section: N Ovcharovamentioning

confidence: 98%

“…Finally, we note that the existence of a solution to problem , respectively , relies on the pseudomonotonicity of the nonsmooth boundary functional and has been investigated in . We recall that the functional

φ : X \times X \to R

, where X is a real reflexive Banach space, is pseudomonotone if

u_{n} ⇀ u

(weakly) in X and

{liminf}_{n \to \infty} φ (u_{n}, u) \geq 0

imply

{limsup}_{n \to \infty} φ (u_{n}, v) \leq φ (u, v)

for all v ∈ X .…”

Section: Boundary Integral Operator Formulationmentioning

confidence: 99%

See 1 more Smart Citation

On the coupling of regularization techniques and the boundary element method for a hemivariational inequality modelling a delamination problem

Ovcharova

2016

Math Methods in App Sciences

Self Cite

View full text Add to dashboard Cite

In this paper, we couple regularization techniques of nondifferentiable optimization with the h-version of the boundary element method (h-BEM) to solve nonsmooth variational problems arising in contact mechanics. As a model example we consider the delamination problem. The variational formulation of this problem leads to a hemivariational inequality (HVI) with a nonsmooth functional defined on the contact boundary. This problem is first regularized and then discretized by a h-BEM. We prove convergence of the h-BEM Galerkin solution of the regularized problem in the energy norm, provide an a-priori error estimate and give a numerical example.

show abstract

“…In this section, we review from [32,34] a class of smoothing approximations for nonsmooth functions that can be re-expressed by means of the plus function p(t) = t + = max{t, 0}. The approximation is based on smoothing of the plus function via convolution.…”

Section: Regularization Of the Nonsmooth Functionalmentioning

confidence: 99%

Coupling regularization and adaptive hp-BEM for the solution of a delamination problem

Ovcharova

Banz

2017

Numer. Math.

Self Cite

View full text Add to dashboard Cite

In this paper, we couple regularization techniques with the adaptive hp-version of the boundary element method (hp-BEM) for the efficient numerical solution of linear elastic problems with nonmonotone contact boundary conditions. As a model example we treat the delamination of composite structures with a contaminated interface layer. This problem has a weak formulation in terms of a nonsmooth variational inequality. The resulting hemivariational inequality (HVI) is first regularized and then, discretized by an adaptive hp-BEM. We give conditions for the uniqueness of the solution and provide an a-priori error estimate. Furthermore, we derive an a-posteriori error estimate for the nonsmooth variational problem based on a novel regularized mixed formulation, thus enabling hp-adaptivity. Various numerical experiments illustrate the behavior, strengths and weaknesses of the proposed high-order approximation scheme.

show abstract

A Study of Regularization Techniques of Nondifferentiable Optimization in View of Application to Hemivariational Inequalities

Cited by 29 publications

References 28 publications

An optimization approach to parameter identification in variational inequalities of second kind

An optimization approach to parameter identification in variational inequalities of second kind

On the coupling of regularization techniques and the boundary element method for a hemivariational inequality modelling a delamination problem

Coupling regularization and adaptive hp-BEM for the solution of a delamination problem

Contact Info

Product

Resources

About