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Stability of stochastic optimization problems – nonmeasurable case. (English) Zbl 1154.90559

Summary: This paper deals with stability of stochastic optimization problems in a general setting. Objective function is defined on a metric space and depends on a probability measure which is unknown, but, estimated from empirical observations. We try to derive stability results without precise knowledge of problem structure and without measurability assumption. Moreover, \(\varepsilon\)-optimal solutions are considered.
The setup is illustrated on consistency of a \(\varepsilon\)-\(M\)-estimator in a linear regression model.

MSC:

90C15 Stochastic programming
90C31 Sensitivity, stability, parametric optimization
62F10 Point estimation
60B05 Probability measures on topological spaces
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References:

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