New metric properties for prox-regular sets
نویسندگان
چکیده
منابع مشابه
Regularization of differential variational inequalities with locally prox-regular sets
This paper studies, for a differential variational inequality involving a locally prox-regular set, a regularization process with a family of classical differential equations whose solutions converge to the solution of the differential variational inequality. The concept of local prox-regularity will be termed in a quantified way, as (r, α)-prox-regularity.
متن کاملSweeping process by prox-regular sets in Riemannian Hilbert manifolds
— In this paper, we deal with sweeping processes on (possibly infinitedimensional) Riemannian Hilbert manifolds. We extend the useful notions (proximal normal cone, prox-regularity) already defined in the setting of a Hilbert space to the framework of such manifolds. Especially we introduce the concept of local prox-regularity of a closed subset in accordance with the geometrical features of th...
متن کاملNonlocal-interaction equations on uniformly prox-regular sets
We study the well-posedness of a class of nonlocal-interaction equations on general domains Ω⊂Rd , including nonconvex ones. We show that under mild assumptions on the regularity of domains (uniform prox-regularity), for λ -geodesically convex interaction and external potentials, the nonlocal-interaction equations have unique weak measure solutions. Moreover, we show quantitative estimates on t...
متن کاملLyapunov functions for evolution variational inequalities with locally prox-regular sets
This paper is devoted on the one hand to the study of specific properties of an evolution variational inequality, holding in the Hilbert setting. We give on the other hand a general criterion for Lyapunov pairs of this dynamical system and some results on the asymptotic behaviour of the solution. Key-words: Differential inclusions Evolution variational inequalities Proximal normal cone Uniforml...
متن کاملExistence Theorems for Some Systems of Quasi–variational Inequalities Problems on Uniformly Prox–regular Sets
In this paper, some systems of quasi-variational inequality problems are considered on a class of nonconvex sets, as uniformly prox-regular sets. Some sufficient conditions for the existence solution of the considered problems are provided. Also, some interesting remarks are discussed. The results which are presented in this paper are more general, and may be viewed as an extension, improvement...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematical Programming
سال: 2020
ISSN: 0025-5610,1436-4646
DOI: 10.1007/s10107-020-01525-x