On the algorithmic solution of optimization problems subject to probabilistic/robust (probust) constraints
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AbstractWe present an adaptive grid refinement algorithm to solve probabilistic optimization problems with infinitely many random constraints. Using a bilevel approach, we iteratively aggregate inequalities that provide most information not in a geometric but in a probabilistic sense. This conceptual idea, for which a convergence proof is provided, is then adapted to an implementable algorithm. The efficiency of our approach when compared to naive methods based on uniform grid refinement is illustrated for a numerical test example as well as for a water reservoir problem with joint probabilistic filling level constraints.
2008 ◽
Vol 34
(1)
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pp. 8-13
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1997 ◽
Vol 24
(4)
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pp. 375-392
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Keyword(s):
2014 ◽
Vol 18
(5)
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pp. 625-636
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