Robust Solutions of Optimization Problems Affected by Uncertain Probabilities

Robust Solutions of Optimization Problems Affected by Uncertain Probabilities

2011 | Ben-Tal, A.; den Hertog, D.; De Waegenaere, A.M.B.; Melenberg, B.; Rennen, G.
This paper focuses on robust linear optimization problems with uncertainty regions defined by $\phi$-divergences, such as chi-squared, Hellinger, and Kullback-Leibler divergences. The authors show that these uncertainty regions naturally arise as confidence sets when the uncertain parameters are probability vectors. They demonstrate that the robust counterpart of a linear optimization problem with $\phi$-divergence uncertainty is tractable for most choices of $\phi$ typically considered in the literature. The paper extends these results to nonlinear optimization problems and provides several applications, including an asset pricing example and a numerical multi-item newsvendor example. The authors also discuss related research and present a detailed derivation of the robust counterparts for problems with $\phi$-divergence uncertainty regions, showing that the robust counterpart can be reformulated as a tractable problem for various choices of $\phi$.This paper focuses on robust linear optimization problems with uncertainty regions defined by $\phi$-divergences, such as chi-squared, Hellinger, and Kullback-Leibler divergences. The authors show that these uncertainty regions naturally arise as confidence sets when the uncertain parameters are probability vectors. They demonstrate that the robust counterpart of a linear optimization problem with $\phi$-divergence uncertainty is tractable for most choices of $\phi$ typically considered in the literature. The paper extends these results to nonlinear optimization problems and provides several applications, including an asset pricing example and a numerical multi-item newsvendor example. The authors also discuss related research and present a detailed derivation of the robust counterparts for problems with $\phi$-divergence uncertainty regions, showing that the robust counterpart can be reformulated as a tractable problem for various choices of $\phi$.
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