  A class of evolution quasistatic systems which leads, after a suitable time
discretization, to recursive nonlinear programs, is considered and optimal
control or identification problems governed by such systems are investigated.
The resulting problem is an evolutionary Mathematical Programs with Equilibrium
Constraints (MPEC). A subgradient information of the (in general nonsmooth)
composite objective function is evaluated and the problem is solved by the
Implicit programming approach. The abstract theory is illustrated on an
identification problem governed by delamination of a unilateral adhesive
contact of elastic bodies discretized by finite-element method in space and a
semi-implicit formula in time. Being motivated by practical tasks, an
identification problem of the fracture toughness and of the elasticity moduli
of the adhesive is computationally implemented and tested numerically on a
two-dimensional example. Other applications including frictional contacts or
bulk damage, plasticity, or phase transformations are outlined.
