Composition duality methods for evolution mixed variational inclusions

Evolution Mixed Variational Inclusions with Optimal Control

“…Hence, by dualization of the dual inclusions of problem (M), and the validity of (18) in its equivalence sense, due to composition duality relations (20), Theorem 7 applies then, additionally, in a sufficiency sense (Alduncin, G., 2007b; Theorem 2.2). That is, the following alternative primal evolution duality principle holds true.…”

“…Here, we follow our previous work on evolution mixed variational inclusions (Alduncin, G., 2007b), in an abstract sense of constrained initial boundary value problems.…”

“…As in the primal case, for a complementary dual duality principle to evolution mixed state inclusion (M * ), we apply the composition duality methodology of (Alduncin, G., 2007b). First, we give a compositional interpretation of primal admissibility characterization (25), based on the next compositional result (Alduncin, G., 2011b).…”

“…For a mixed variational structure of the governing state model, and for computational purposes, imposed constraints are handled via compositional dualization. The state system solvability is analized on the basis of composition duality principles in the sense of (Alduncin, G., 2007a(Alduncin, G., , 2007b(Alduncin, G., , 2011b, which lead to a primal-dual variational analysis.…”

“…Here, in accordance with (Alduncin, G., 2007a(Alduncin, G., , 2007b(Alduncin, G., , 2011b, we consider primal as well as dual evolution mixed variational inclusions, since both formulations are of relevant importance in computational mechanics. Through the sequel, applications to nonlinear diffusion constrained processes, and quasistatic elastoviscoplastic variational contact problems, exemplify the control theory.…”