Conditioning of linear-quadratic two-stage stochastic optimization problems

Abstract

In this paper a condition number for linear-quadratic two-stage stochastic optimization problemsis introduced as the Lipschitz modulus of the multifunction assigning to a (discrete) probabilitydistribution the solution set of the problem. Being the outer norm of the Mordukhovich coderivativeof this multifunction, the condition number can be estimated from above explicitly in terms of theproblem data by applying appropriate calculus rules. Here, a chain rule for the extended partialsecond-order subdifferential recently proved by Mordukhovich and Rockafellar plays a crucial role.The obtained results are illustrated for the example of two-stage stochastic optimization problemswith simple recourse.