-
作者：Conforti, Michele; Di Summa, Marco; Faenza, Yuri
作者单位：University of Padua; Columbia University
摘要：A celebrated theorem of Balas gives a linear mixed-integer formulation for the union of two nonempty polytopes whose relaxation gives the convex hull of this union. The number of inequalities in Balas formulation is linear in the number of inequalities that describe the two polytopes and the number of variables is doubled. In this paper we show that this is best possible: in every dimension there exist two nonempty polytopes such that if a formulation for the convex hull of their union has a n...
-
作者：Sun, Jie; Yang, Xinmin; Yao, Qiang; Zhang, Min
作者单位：Curtin University; National University of Singapore; Chongqing Normal University; East China Normal University; New York University; NYU Shanghai; Chinese Academy of Sciences; Xinjiang Institute of Ecology & Geography, CAS; Chinese Academy of Sciences; University of Chinese Academy of Sciences, CAS
摘要：This paper begins with a study on the dual representations of risk and regret measures and their impact on modeling multistage decision making under uncertainty. A relationship between risk envelopes and regret envelopes is established by using the Lagrangian duality theory. Such a relationship opens a door to a decomposition scheme, called progressive hedging, for solving multistage risk minimization and regret minimization problems. In particular, the classical progressive hedging algorithm ...
-
作者：Burke, James V.; Chen, Xiaojun; Sun, Hailin
作者单位：University of Washington; University of Washington Seattle; Hong Kong Polytechnic University; Nanjing Normal University
摘要：The subdifferential calculus for the expectation of nonsmooth random integrands involves many fundamental and challenging problems in stochastic optimization. It is known that for Clarke regular integrands, the Clarke subdifferential of the expectation equals the expectation of their Clarke subdifferential. In particular, this holds for convex integrands. However, little is known about the calculation of Clarke subgradients for the expectation of non-regular integrands. The focus of this contr...
