Kavli Affiliate: Jia Liu
| First 5 Authors: Yu Mei, Jia Liu, Zhiping Chen, ,
| Summary:
We consider a distributionally robust second-order stochastic dominance
constrained optimization problem. We require the dominance constraints hold
with respect to all probability distributions in a Wasserstein ball centered at
the empirical distribution. We adopt the sample approximation approach to
develop a linear programming formulation that provides a lower bound. We
propose a novel split-and-dual decomposition framework which provides an upper
bound. We establish quantitative convergency for both lower and upper
approximations given some constraint qualification conditions. To efficiently
solve the non-convex upper bound problem, we use a sequential convex
approximation algorithm. Numerical evidences on a portfolio selection problem
valid the convergency and effectiveness of the proposed two approximation
methods.
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