We study an adiabatic variant of the variational quantum eigensolver (VQE) in which VQE is performed iteratively for a sequence of Hamiltonians along an adiabatic path. We derive the conditions under which gradient-based optimization successfully prepares the adiabatic ground states. These conditions define a trainable tracking region. Additionally, when combined with a gap lower bound, energy-standard-deviation measurements certify eigenstate accuracy at runtime and verify convergence to the global optimum.