Conditioning of linear-quadratic two-stage stochastic optimization problems
- Emich, Konstantin
- Henrion, René
- Römisch, Werner
2010 Mathematics Subject Classification
- 90C15 90C31 49K40
- Stochastic optimization, two-stage linear-quadratic problems, conditioning, coderivative calculus, simple recourse
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 can be estimated from above explicitly in terms of the problem data by applying appropriate calculus rules. Here, a chain rule for the extended partial second-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 problems with simple recourse.
- Math. Program., 148 (2014) pp. 201--221.