Composition duality methods in contact mechanics

Abstract

Composition duality methods in the context of optimization problems in mechanics have been the basis for analysis and approximation of minimization and related minimax problems, as studied by Ekeland and Temam [1]. Abstract convex functionals of the type J(ν) = F(ν)+G(Λ ν), ν ∈ V, have been considered on a reflexive Banach space V. Associated two-field Lagrangians have been of the type L(ν, q ^*) = F(ν) – G ^*(q ^*)+ < (q ^*), Λ ν >Y, (ν, q ^*) ∈ V × Y ^*, Y ^* denoting the topological dual of another reflexive Banach space Y. Then,corresponding duality principles establish conditions for the solvability equivalence of the primal and mixed optimality condition problems.