Two-level optimization with approximate solutions in the lower level

If the paper wants to apply iterative solution procedures of nonlinear optimization for solving the upper level of a two-level optimization problem, at each step the required probelm data must be generated by solving the lower level for the actual parameter value. For the class of gradient-type methods it discusses some ideas, how the accuracy in the lower level can be controlled to ensure the convergence in the upper level. The present paper supplements results of a book of Gol’stein and Tretyakov from 1989.