Distributionally robust joint chance constraints with second-order moment information
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789 citations
Additional excerpts
...Robust optimization, ambiguous probability distributions, conic optimization....
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742 citations
505 citations
Additional excerpts
...Key words : distributionally robust optimization; data-driven; ambiguity set; worst-case distribution MSC2000 subject classification : Primary: 90C15; secondary: 90C46 OR/MS subject classification : Primary: programming: stochastic 1....
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437 citations
Cites background or methods from "Distributionally robust joint chanc..."
...[39], we develop an equivalent reformulation for the joint DCCs....
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...[39], we propose an algorithm based on iteratively solving two convex optimization problems (hereafter denoted as iterative convex optimization) to solve [DCCP]....
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...[39], we develop a more general approach to obtain the result, which can easily be extended to obtain reformulations under other forms of moment information (e....
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...[39] consider exact solution approaches for the joint chance constraint version of DRCC....
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...[39] develop an equivalent reformulation for the single DCCs and a worst-case CVaR-based approximation for the joint DCCs....
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348 citations
Cites background from "Distributionally robust joint chanc..."
...[345] study a safe approximation to distributionally robust individual and joint chance constraints based on the worst-case CVaR....
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...[345] show that the CVaR approximation is exact for joint chance constraints whose constraint functions depend linearly on ξ̃....
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References
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"Distributionally robust joint chanc..." refers methods in this paper
...To this end, we first recall the definition of CVaR due to Rockafellar and Uryasev [24]....
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1,569 citations
"Distributionally robust joint chanc..." refers methods in this paper
...where the interchange of the maximization and minimization operations is justified by a stochastic saddle point theorem due to Shapiro and Kleywegt [26], see also Delage and Ye [11] or Natarajan et al....
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1,535 citations
"Distributionally robust joint chanc..." refers background in this paper
...In this case, the chance constrained problem becomes a tractable second-order cone program (SOCP), which can be solved in polynomial time, see Alizadeh and Goldfarb [1]....
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1,122 citations
"Distributionally robust joint chanc..." refers background in this paper
...Recently, Calafiore and Campi [5] as well as Luedtke and Ahmed [17] have proposed to replace the chance constraint (2) by a pointwise constraint that must hold at a finite number of sample points drawn randomly from the distribution Q....
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...Calafiore and Campi [5] showed that one requires O(n/ ) samples to guarantee that a solution of the approximate problem is feasible in the original chance constrained program....
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