Conditioning of linear-quadratic two-stage stochastic optimization problems

In this paper a condition number for linear-quadratic two-stage stochastic optimization problems is introduced as the Lipschitz modulus of the multifunction assigning to a (discrete) probability distribution the solution set of the problem. Being the outer norm of the Mordukhovich coderivative of this multifunction, the condition number canbe estimated fromabove explicitly in termsof the problemdata by applying appropriate calculus rules. Here, a chain rule for the extended partial second-order subdifferential recently proved byMordukhovich and Rockafellar plays a crucial role. Theobtained results are illustrated for the example of two-stage stochastic optimization problems with simple recourse.