Risk-Averse Stochastic Programming and Distributionally Robust Optimization Via Operator Splitting

This work deals with a broad class of convex optimization problems under uncertainty. The approach is to pose the original problem as one of finding a zero of the sum of two appropriate monotone operators, which is solved by the celebrated Douglas-Rachford splitting method. The resulting algorithm,...

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Vydáno v:Set-valued and variational analysis Ročník 29; číslo 4; s. 861 - 891
Hlavní autor: de Oliveira, Welington
Médium: Journal Article
Jazyk:angličtina
Vydáno: Dordrecht Springer Netherlands 01.12.2021
Springer Nature B.V
Springer
Témata:
Algorithms
Ambiguity
Analysis
Computational geometry
Convexity
Mapping
Mathematics
Mathematics and Statistics
Optimization
Risk
Robustness
Splitting
Stochastic programming
Subspaces
Splitting methods
49J53
49J52
90C25
Progressive hedging
Distributionally robust optimization
90C15
Multistage stochastic programs
ADMM
ISSN:1877-0533, 1877-0541
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Shrnutí:This work deals with a broad class of convex optimization problems under uncertainty. The approach is to pose the original problem as one of finding a zero of the sum of two appropriate monotone operators, which is solved by the celebrated Douglas-Rachford splitting method. The resulting algorithm, suitable for risk-averse stochastic programs and distributionally robust optimization with fixed support, separates the random cost mapping from the risk function composing the problem’s objective. Such a separation is exploited to compute iterates by alternating projections onto different convex sets. Scenario subproblems, free from the risk function and thus parallelizable, are projections onto the cost mappings’ epigraphs. The risk function is handled in an independent and dedicated step consisting of evaluating its proximal mapping that, in many important cases, amounts to projecting onto a certain ambiguity set. Variables get updated by straightforward projections on subspaces through independent computations for the various scenarios. The investigated approach enjoys significant flexibility and opens the way to handle, in a single algorithm, several classes of risk measures and ambiguity sets.
Bibliografie:ObjectType-Article-1
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ISSN:1877-0533
1877-0541
DOI:10.1007/s11228-021-00600-5