two-level value function – Optimization Online

Stability analysis for two-level value functions and application to numerically solve a pessimistic bilevel program

Published: 2025/05/22

Bilevel Optimization Karush-Kuhn-Tucker reformulation, necessary optimality conditions, pessimistic bilevel optimization, Scholtes relaxation, two-level value function

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 … Read more

Sensitivity analysis for two-level value functions with applications to bilevel programming

Published: 2011/11/03

Stephan Dempe

Boris S. Mordukhovich

Alain Zemkoho

Nonlinear Optimization, Nonsmooth Optimization, Unconstrained Optimization bilevel optimization, coderivative, lipschitz-like property, mpcc value functions, optimality conditions, sensitivity analysis, two-level value function

This paper contributes to a deeper understanding of the link between a now conventional framework in hierarchical optimization spread under the name of the optimistic bilevel problem and its initial more dicult formulation that we call here the original optimistic bilevel optimization problem. It follows from this research that, although the process of deriving necessary … Read more