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 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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