Some stability results are presented for a two-level value function, which is the optimal value
function of a parametric optimization problem constrained by the optimal solution set of another
parameteric optimization problem. It is then shown how to use these stability results to write down
(and subsequently compute) stationary points for a pessimistic bilevel optimization problem. It
is also demonstrated how the corresponding Scholtes relaxation–based numerical process can be
used to calculate local and global–type optimal solutions for the pessimistic bilevel program if one
is equipped with a solver for minmax programs involving coupled inner constraints.
Citation
Alain Zemkoho (2025). Stability analysis for two-level value functions and application to numerically solve a pessimistic bilevel program, Encyclopedia of Optimization: https://doi.org/10.1007/978-3-030-54621-2