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作者：Baveja, Alok; Chavan, Amit; Nikiforov, Andrei; Srinivasan, Aravind; Xu, Pan
作者单位：Rutgers University System; Rutgers University New Brunswick; Rutgers University System; Rutgers University Camden; Rutgers University New Brunswick; University System of Maryland; University of Maryland College Park; New Jersey Institute of Technology
摘要：Real-world network-optimization problems often involve uncertain parameters during the optimization phase. Stochastic optimization is a key approach introduced in the 1950s to address such uncertainty. This paper presents improved upper bounds on the number of samples required for the sample-average approximation method in stochastic optimization. It enhances the sample complexity of existing approaches in this setting, providing faster approximation algorithms for any method that employs this...
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作者：Chen, Rui; Gunluk, Oktay; Lodi, Andrea
作者单位：Cornell University
摘要：Dantzig-Wolfe (DW) decomposition is a well-known technique in mixedinteger programming (MIP) for decomposing and convexifying constraints to obtain potentially strong dual bounds. We investigate cutting planes that can be derived using the DW decomposition algorithm and show that these cuts can provide the same dual bounds as DW decomposition. More precisely, we generate one cut for each DW block, and when combined with the constraints in the original formulation, these cuts imply the objectiv...
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作者：Zhen, Jianzhe; Kuhn, Daniel; Wiesemann, Wolfram
作者单位：Chinese Academy of Sciences; University of Chinese Academy of Sciences, CAS; Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; Imperial College London
摘要：Robust optimization and distributionally robust optimization are modeling paradigms for decision making under uncertainty where the uncertain parameters are only known to reside in an uncertainty set or are governed by any probability distribution from within an ambiguity set, respectively, and a decision is sought that minimizes a cost function under the most adverse outcome of the uncertainty. In this paper, we develop a rigorous and general theory of robust and distributionally robust nonli...
