Risk minimization, regret minimization and progressive hedging algorithms
MetadataShow full item record
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.
Showing items related by title, author, creator and subject.
A new interpretation of the progressive hedging algorithm for multistage stochastic minimization problemsSun, Jie ; Xu, Honglei ; Zhang, Min (2020)The progressive hedging algorithm of Rockafellar and Wets for multistage stochastic programming problems could be viewed as a two-block alternating direction method of multipliers. This correspondence brings in some useful ...
A Model of Multistage Risk-Averse Stochastic Optimization and its Solution by Scenario-Based Decomposition AlgorithmsZhang, M.; Hou, L.; Sun, Jie ; Yan, A. (2020)Stochastic optimization models based on risk-averse measures are of essential importance in financial management and business operations. This paper studies new algorithms for a popular class of these models, namely, the ...
Zhang, M.; Sun, Jie ; Xu, Honglei (2019)A model of a two-stage N-person noncooperative game under uncertainty is studied, in which at the first stage each player solves a quadratic program parameterized by other players’ decisions and then at the second stage ...