A characterization of tyhonov well-posedness for minimum problems, with applications to variational inequalities (∗)

In this paper, we generalize the concept of well-posedness to a system of hemivariational inequalities in Banach space. By introducing several concepts of well-posedness for systems of hemivariational inequalities considered, we establish some metric characterizations of well-posedness and prove some equivalence results of strong (generalized) well-posedness between a system of hemivariational inequalities and its derived system of inclusion problems.

Section: Introductionmentioning

confidence: 99%

Equivalence of well-posedness between systems of hemivariational inequalities and inclusion problems

Wang¹,

Xiao²,

Wang³

et al. 2016

“…By means of Ekeland's variational principle, Lucchetti and Patrone [21] first introduced the concept of wellposedness for a variational inequality and proved some related results. Fang et al [8,9] generalized two kinds of well-posedness for a mixed variational inequality problem in Banach space, respectively.…”

Section: Introductionmentioning

confidence: 99%

On the well-posedness of generalized hemivariational inequalities and inclusion problems in Banach spaces

Ceng¹,

Liou²,

溫慶豐³

et al. 2016

In the present paper, we generalize the concept of well-posedness to a generalized hemivariational inequality, give some metric characterizations of the α-well-posed generalized hemivariational inequality, and derive some conditions under which the generalized hemivariational inequality is strongly α-well-posed in the generalized sense. Also, we show that the α-well-posedness of the generalized hemivariational inequality is equivalent to the α-well-posedness of the corresponding inclusion problem.

“…After that, various kinds of results concerned with well-posedness for many optimization problems were established and various kinds of well-posedness for optimization problems and their related ones were studied extensively in recent years by a large number of researchers in many fields; see e.g., [8,15,21,42] and the references therein. In 1981, Lucchetti and Patrone [23] extended the notion of well-posedness for optimization problems to a variational inequality for the first time. By using Ekeland's theorem, they gave a characterization of Tykhonov's well-posedness for a minimizing problem with a convex lower semi-continuous function on a closed convex set.…”

Section: Introductionmentioning

confidence: 99%

Well-posedness for systems of time-dependent hemivariational inequalities in Banach spaces

Ceng¹,

Liou²,

Yao³

et al. 2017

In this paper, we generalize the concept of α-well-posedness to a system of time-dependent hemivariational inequalities without Volterra integral terms in Banach spaces. We establish some metric characterizations of α-well-posedness and prove some equivalence results of strong α-well-posedness (resp., in the generalized sense) between a system of time-dependent hemivariational inequalities and its derived system of inclusion problems.