A class of evolution variational inequalities with nonconvex constraints. (3rd October 2019)

• Record Type: Journal Article
• Authors: Peng, Zijia; Gasiński, Leszek; Migórski, Stanisław; Ochal, Anna
• Is Part Of: Optimization. Volume 68:Number 10(2019)
• Page Start: 1881
• Page End: 1895
• Publication Date: 2019-10-03
• Subjects: Variational inequality -- hemivariational inequality -- L-pseudomonotone operator -- operator inclusion -- generalized gradient; 47J35 -- 47J20 -- 47J22 -- 35K86; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2018.1476861
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: We study a nonconvex constrained evolution problem for a set being the union of a finite number of convex sets. The problem generalizes the classical parabolic variational inequality of the second kind and contains an operator of L - ( S ) + -type. The existence result for this problem is proved using a variational-hemivariational inequality approach, a surjectivity theorem for multivalued pseudomonotone operators in a reflexive Banach space and a penalization method in which a small parameter does not have to tend to zero.