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

Identification of some nonsmooth evolution systems with illustration on adhesive contacts at small strains