Universal Confidence Sets for Solutions of Optimization Problems

Vogel, Silvia GND

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 con¯dence 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 con¯dence sets for constrained estimation problems.

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Vogel, Silvia: Universal Confidence Sets for Solutions of Optimization Problems. 2006.

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