Universal Confidence Sets for Solutions of Optimization Problems

We consider random approximations to deterministic optimization problems. The objective function and the constraint set can be approximated simultaneously. Relying on concentration-of-measure results we derive universal confidence sets for the constraint set, the optimal value and the solution set. Special attention is paid to solution sets which are not single-valued. Many statistical estimators being solutions to random optimization problems, the approach can also be employed to derive confidence sets for constrained estimation problems.

• Type: Journal
• Year: 2008
• Where: SIAMJO
• Authors: Silvia Vogel
• Keywords: Many Statistical Estimators, Optimization Problems, Random Approximations, SIAMJO 2008