Risk minimization, regret minimization and progressive hedging algorithms
成果类型：
Article
署名作者：
Sun, Jie; Yang, Xinmin; Yao, Qiang; Zhang, Min
署名单位：
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
刊物名称：
MATHEMATICAL PROGRAMMING
ISSN/ISSBN：
0025-5610
DOI：
10.1007/s10107-020-01471-8
发表日期：
2020
页码：
509-530
关键词：
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 is modified in order to handle a new class of linkage constraints that arises from reformulations and other applications of risk and regret minimization problems. Numerical results are provided to show the efficiency of the progressive hedging algorithms.