Qualitative Stability of Convex Programs with Probabilistic Constraints
- Henrion, René
2010 Mathematics Subject Classification
- 90C15 90C31
- stochastic programming, probabilistic constraints, qualitative stability, r-concave measures
We consider convex stochastic optimization problems with probabilistic constraints which are defined by so-called r-concave probability measures. Since the true measure is unknown in general, the problem is usually solved on the basis of estimated approximations, hence the issue of perturbation analysis arises in a natural way. For the solution set mapping and for the optimal value function, stability results are derived. In order to include the important class of empirical estimators, the perturbations are allowed to be arbitrary in the space of probability measures (in contrast to the convexity property of the original measure). All assumptions relate to the original problem. Examples show the necessity of the formulated conditions and illustrate the sharpness of results in the respective settings.
- In V.H. Nguyen, J. -J. Strodiot and P. Tossings (eds.): Optimization (Lect. Notes in Economics and Mathematical Systems, Vol. 481), (2000), pp. 164-180