Stochastic linear programming with a distortion risk constraint. Coherent distortion risk measures are applied to capture the possible violation of a restriction in linear optimization problems whose parameters are uncertain. Each risk constraint induces an uncertainty set of coefficients, which is proved to be a weighted-mean trimmed region. Thus, given a sample of the coefficients, an uncertainty set is a convex polytope that can be exactly calculated. We construct an efficient geometrical algorithm to solve stochastic linear programs that have a single distortion risk constraint. The algorithm is available as an R-package. The algorithm’s asymptotic behavior is also investigated, when the sample is i.i.d. from a general probability distribution. Finally, we present some computational experience.
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References in zbMATH (referenced in 4 articles , 1 standard article )
Showing results 1 to 4 of 4.
- Dyckerhoff, Rainer; Mozharovskyi, Pavlo: Exact computation of the halfspace depth (2016)
- Postek, Krzysztof; den Hertog, Dick; Melenberg, Bertrand: Computationally tractable counterparts of distributionally robust constraints on risk measures (2016)
- Bazovkin, Pavel; Mosler, Karl: A general solution for robust linear programs with distortion risk constraints (2015)
- Mosler, Karl; Bazovkin, Pavel: Stochastic linear programming with a distortion risk constraint (2014)