Abstract
If we want to apply iterative solution procedures of nonlinear optimization for solving the upper level of a two-level optimization problem, at each step the required problem data must be generated by solving the lower level for the actual parameter value. For the class of gradient-type methods we discuss 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.
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Tammer, K. Two-level optimization with approximate solutions in the lower level. ZOR - Mathematical Methods of Operations Research 41, 231–249 (1995). https://doi.org/10.1007/BF01432657
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DOI: https://doi.org/10.1007/BF01432657