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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...
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作者：Curmei, Mihaela; Hall, Georgina
作者单位：University of California System; University of California Berkeley; INSEAD Business School
摘要：We present a hierarchy of semidefinite programs (SDPs) for the problem of fitting a shape-constrained (multivariate) polynomial to noisy evaluations of an unknown shape-constrained function. These shape constraints include convexity or monotonicity over a box. We show that polynomial functions that are optimal to any fixed level of our hierarchy form a consistent estimator of the underlying shape-constrained function. As a by-product of the proof, we establish that sum of squares-convex polyno...
