Solvability and optimization for a class of mixed variational problems. (3rd May 2020)

• Record Type: Journal Article
• Authors: Matei, Andaluzia; Sofonea, Mircea
• Is Part Of: Optimization. Volume 69:Number 5(2020)
• Page Start: 1097
• Page End: 1116
• Publication Date: 2020-05-03
• Subjects: Mixed variational problem -- Lagrange multiplier -- optimization problem -- Hencky material -- antiplane frictional contact problem -- weak solution; 35J65 -- 49J20 -- 65K10 -- 49K27 -- 49J40 -- 74M10 -- 74M15; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2019.1676242
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: We consider an abstract mixed variational problem governed by a nonlinear operator A and a bifunctional J, in a real reflexive Banach space X . The operator A is assumed to be continuous, Lipschitz continuous on each bounded subset of X, and generalized monotone. First, we pay attention to the unique solvability of the problem. Next, we prove a continuous dependence result of the solution with respect to the data. Based on this result, we prove the existence of at least one solution for an associated optimization problem. Finally, we apply our abstract results to the well-posedness and the optimization of an antiplane frictional contact model for nonlinearly elastic materials of Hencky type.